条件概率教案1

条件概率1 条 件 概 率 东北师范大学数学与统计学院 【课题来源】 3第二章第二节的第一课时。条件概率是新课程标准下数学本课选自新人教版高中数学选修2- 教材中涉及的一个重要知识点，本节内容承前启后，就其本身来讲，本课虽为选修内容，但从学生的角度讲仍占有较高的地位，使学生从另一个视角理解概率，可使其深刻理解概率源于生活，应用于生活，进而产生浓厚的数学学习兴趣。 【教学目标】 知识与技能: 通过现实情境的探究，理解条件概率的概念及其计算公式，并能简单地应用公式进行问题解决。 过程与方法: 1(通过对条件概率计算公式的探究，渗透归纳思维和数形结合的思想方法，培养学生观察、归纳、抽象的能力和直观能力; 2(通过知识的探究过程培养学生细心观察、认真、严谨论证的良好思维习惯，让学生感知从具体到抽象，从特殊到一般，从感性到理性的认知过程。 情感、态度与价值观: 结合现实情境，渗透概率思想，学会透过现象看本质，加强数学应用意识和数学审美能力的培养，激发学生学习数学的兴趣;对学生进行辨证唯物主义教育，培养学生坚持实事求是的态度、锲而不舍的科学精神。 【教学重难点】 教学重点:条件概率的定义及其计算公式。 教学难点:条件概率与概率的区别与联系。 解决难点的关键:弄清楚“事件A发生”、“事件A发生并且事件B也发生”以及“事件B在事件A发生的条件下发生”的概率之间的关系和区别。 【教法分析】 从学生的认知规律出发，结合问题情境，通过探究、交流合作，运用讲授法、讨论法、阅读指导法充分调动学生的积极性，发挥学生的主体作用，在讲授过程中善于解疑、设疑、激疑，通过合情推理与演绎推理的思维过程，培养学生的归纳思维，让学生感知从具体到抽象，从特殊到一般，从感性到理性的认知过程。 of support and hanger. Cable hole plugging gaps should use qualified fireproof materials, block surface should have sufficient strength, surface appearance. When cables pass through the firewall, of lax structure of local fire safety clamps. Thermoplastics production, to comply with the process, no bubbles in the thermoplastics pipes, linear nose consistent with the core wire specifications, contact is good, no cracks, break. Tinned copper nose clean solder full exterior surface is smooth without burrs. Control cable Assembly should be fastened, dense, solid, clean, and beautiful. Secondary wiring the cable terminations should be arranged by the actual location of the device line cards, the wiring from the upper to the lower, from left to right in the order. Fixed to maintain consistent spacing between lines, flat, should be around the corner in the same location, same shape, to ensure that the wiring process neater and more elegant. 5 thermal process control measures for quality problems 5.1 control thermal duct system leakage measure to ensure that the use of electric door and actuator installation quality and equipment to the site to check its seal, acceptance, in order to fundamentally solve oil spill problems. Plant for local Panel after installation, in conjunction with the quality Department to check its overall quality, poor-quality parts replacement. Supply good quality of purchasing instrument and ovality of the guarantee instrument tubes as small as possible, selection of high quality, high precision sleeve connector. Instrument pipe welding, construction workers and technicians on every road, every instrument as well recorded and well identified in the instrument, welding welding following the end of each review, responsibility and prevention of welding, welding wrong. Requirements for welding personnel certified, and welding before welding training, select skills good sense to carry out construction, welding quality inspection and acceptance every day to ensure that the welding ... All unreleased material sampling, invited supervision engineers arrived at the scene, after confirmation by the supervising engineer, seal immediately sent authorized bodies in accordance with the requested test indicator test, according to the inspection report and approved by the supervising engineer to review and then transported for the construction. Amount of insulation materials shall 【教学手段】 计算机、投影仪。 【教学过程】 教 学 内 容 师生互动 设计意图 预案: 创 问题情境: 教师:让学生先独立思问题情境的创设贴设 某人有两个孩子，请思考: 考问题。 近生活，能够激起情问题,:他的两个孩子都是男孩的概率是多学生:大胆尝试，给出 答案。 学生探究激情，符境 少, 教师:根据学生讨论、合学生的认知规，问题,:如果他说:“我的大孩子是男孩”，则两 回答情况分析两个问题律，给学生设置认引 个孩子都是男孩的概率是多少, 之间的区别和联系，鼓知冲突。通过学生入 归纳:(预计学生都会凭直觉而出错) 励学生给出条件概率的的困惑体会引出本课 分析问题之间的区别和联系，给出条件概率的 定义，引入新课。 课概念的必要性。 题 定义。 形成概念;条件概率的概念 对于任何两个事件,和,，在已知事件, 发生的条件下，事件,发生的概率叫做条件概 P(BA)率。记作:，读作:,发生的条件下, 的概率。 游戏活动: 抛掷红，蓝两骰子，思考如下问题: 教师:学生能够比较容游戏的设置具有较 预案: 易解决问题。学生:独强的现实情景,增 游问题1:事件,:“蓝色骰子的点数为,或,”概立回答问题1-3。 强学生学习的兴 戏率为多少, 趣,让学生充分感 探问题2:事件,:“两颗骰子的点数之和大于,”受条件概率的本原 究 概率为多少, 的朴素的想法。 ，问题3:事件A和B同时发生的概率为多少呢? 通过相互讨论，加揭变式 : 教师:通过变式同样采 用缩小样本空间的方强学生间的交流与示问题4:在已知事件,发生的条件下，事件,发 法，让学生求出相应的 合作，充分发挥学新生的概率为多少呢, 概率。 生学习的主动性，知 问题5:在已知事件B发生的条件下，事件A学生:分组讨论，积极 Depar in order to fundamentally solve oil spill problems. Plant for local Panel after installation, in conjunction with the qualityure that the use of electric door and actuator installation quality and equipment to the site to check its seal, acceptance, to enser and more elegant. 5 thermal process control measures for quality problems 5.1 control thermal duct system leakage measure ing between lines, flat, should be around the corner in the same location, same shape, to ensure that the wiring process neatt spacf the device line cards, the wiring from the upper to the lower, from left to right in the order. Fixed to maintain consistenened, dense, solid, clean, and beautiful. Secondary wiring the cable terminations should be arranged by the actual location oe fastcracks, break. Tinned copper nose clean solder full exterior surface is smooth without burrs. Control cable Assembly should bocess, no bubbles in the thermoplastics pipes, linear nose consistent with the core wire specifications, contact is good, no the pren cables pass through the firewall, of lax structure of local fire safety clamps. Thermoplastics production, to comply with plugging gaps should use qualified fireproof materials, block surface should have sufficient strength, surface appearance. Whof support and hanger. Cable hole 2eview and then transported for the construction. Amount of insulation materials shallr to raccordance with the requested test indicator test, according to the inspection report and approved by the supervising engineen engineers arrived at the scene, after confirmation by the supervising engineer, seal immediately sent authorized bodies in rvisioing quality inspection and acceptance every day to ensure that the welding ... All unreleased material sampling, invited supeor welding personnel certified, and welding before welding training, select skills good sense to carry out construction, weldnts ftrument, welding welding following the end of each review, responsibility and prevention of welding, welding wrong. Requiremewelding, construction workers and technicians on every road, every instrument as well recorded and well identified in the ins l as possible, selection of high quality, high precision sleeve connector. Instrument pipequality parts replacement. Supply good quality of purchasing instrument and ovality of the guarantee instrument tubes as smal-tment to check its overall quality, poor 让学生对知识进行发生的概率为多少呢, 思考，交流体会。 类比、迁移以及联 想。 学生自己归纳出条探究: 教师:提出问题，让学 件概率的计算公那么请大家观察，以条件概率生找出条件概率公式。 式，便于学生操作学生:小组讨论 P(AB)为讨论对象，其他哪些结论P(BA),P(A)感知，完成条件概 、、P(BA)P(A)P(B) 5率公式第一次认 与有关呢, 与之间的关P(A:B)12 识, 系。 通过几何直观感 直观演示: 学生:归纳总结，教师:知，完成条件概率 教师可以引导学生从集合的观点解释条件概率点拨，强调归纳思想。 公式的可视化认 公式。 知, 教师:利用几何图形，让把对公式的认识由 形式化证明 学生直观理解条件概率 感性上升到理性认的本质属性。 识的高度,让学生由 特殊到一般，从具教师:利用概率公式，形成公式; 体到抽象通过演绎形式化证明。 P(A:B)P(BA),条件概率公式，推理，实现了公式P(A) 的形式化证明，完 >0。 P(A) 成对概念的第三次 认识。 es in rvision engineers arrived at the scene, after confirmation by the supervising engineer, seal immediately sent authorized bodiing quality inspection and acceptance every day to ensure that the welding ... All unreleased material sampling, invited supe, weldents for welding personnel certified, and welding before welding training, select skills good sense to carry out constructionstrument, welding welding following the end of each review, responsibility and prevention of welding, welding wrong. Requiremthe int pipe welding, construction workers and technicians on every road, every instrument as well recorded and well identified in of the guarantee instrument tubes as small as possible, selection of high quality, high precision sleeve connector. Instrumenquality parts replacement. Supply good quality of purchasing instrument and ovality -Department to check its overall quality, poor in order to fundamentally solve oil spill problems. Plant for local Panel after installation, in conjunction with the qualityance, to ensure that the use of electric door and actuator installation quality and equipment to the site to check its seal, accepter and more elegant. 5 thermal process control measures for quality problems 5.1 control thermal duct system leakage measure s neatt spacing between lines, flat, should be around the corner in the same location, same shape, to ensure that the wiring procesf the device line cards, the wiring from the upper to the lower, from left to right in the order. Fixed to maintain consistention oe fastened, dense, solid, clean, and beautiful. Secondary wiring the cable terminations should be arranged by the actual locacracks, break. Tinned copper nose clean solder full exterior surface is smooth without burrs. Control cable Assembly should bd, no the process, no bubbles in the thermoplastics pipes, linear nose consistent with the core wire specifications, contact is gooen cables pass through the firewall, of lax structure of local fire safety clamps. Thermoplastics production, to comply with t strength, surface appearance. Whof support and hanger. Cable hole plugging gaps should use qualified fireproof materials, block surface should have sufficien3r to review and then transported for the construction. Amount of insulation materials shallaccordance with the requested test indicator test, according to the inspection report and approved by the supervising enginee 问题探究: 前后呼应，让学生 应 以下哪个问题是条件概率问题,如果是， 找出条件概率问题用 请应用条件概率公式计算之。 学生:独立完成。 中所具有的特点和新某人有两个孩子，请思考: 性质，巩固条件概知 问题,:他的两个孩子都是男孩的概率是多教师:点拨。 率的概念与计算方，少, 法，建立较完整的归 问题,:如果他说:“我的大孩子是男孩”，则两 认知结构，揭示条纳 个孩子都是男孩的概率是多少, 件概率的本质。 总 深度挖掘: 结 P(B)、P(A?B)与P(B|A)三个概率之间的区别与 教学的反馈与评 联系。 价，学生消化所学 知识。 请同学们总结这节课都有哪些收获, 教师:总结。 【板书设计】 2.2.1条件概率 一(条件概率的定义 在已知事件A发生的条件下， 归纳公式 整个事件空间 事件B发生的概率叫做条件概率。 公式推广 五个问题的结果 记作:P(B|A )， Venn图解释 二(条件概率的计算公式 P(A:B)思考题 P(B|A), , P(A),0P(A) or welding personnel certified, and welding before welding training, select skills good sense to carry out construction, weldnts ftrument, welding welding following the end of each review, responsibility and prevention of welding, welding wrong. Requiremewelding, construction workers and technicians on every road, every instrument as well recorded and well identified in the ins l as possible, selection of high quality, high precision sleeve connector. Instrument pipequality parts replacement. Supply good quality of purchasing instrument and ovality of the guarantee instrument tubes as smal-tment to check its overall quality, poorDepar in order to fundamentally solve oil spill problems. Plant for local Panel after installation, in conjunction with the qualityure that the use of electric door and actuator installation quality and equipment to the site to check its seal, acceptance, to enser and more elegant. 5 thermal process control measures for quality problems 5.1 control thermal duct system leakage measure ing between lines, flat, should be around the corner in the same location, same shape, to ensure that the wiring process neatt spacf the device line cards, the wiring from the upper to the lower, from left to right in the order. Fixed to maintain consistenened, dense, solid, clean, and beautiful. Secondary wiring the cable terminations should be arranged by the actual location oe fastcracks, break. Tinned copper nose clean solder full exterior surface is smooth without burrs. Control cable Assembly should bocess, no bubbles in the thermoplastics pipes, linear nose consistent with the core wire specifications, contact is good, no the pren cables pass through the firewall, of lax structure of local fire safety clamps. Thermoplastics production, to comply with plugging gaps should use qualified fireproof materials, block surface should have sufficient strength, surface appearance. Whof support and hanger. Cable hole 4eview and then transported for the construction. Amount of insulation materials shallr to raccordance with the requested test indicator test, according to the inspection report and approved by the supervising engineen engineers arrived at the scene, after confirmation by the supervising engineer, seal immediately sent authorized bodies in rvisioing quality inspection and acceptance every day to ensure that the welding ... All unreleased material sampling, invited supe 【教学设计说明】 《条件概率》教学设计说明 一、教学内容的分析 条件概率，对于学生来讲是全新的学习内容，因而在给出定义之前要给学生一个直观印象，从生活中先感知条件概率，再引入定义;随后，即通过问题串，让学生讨论、观察，自行发现条件概率的计算公式，便于学生操作感知，完成条件概率公式第一次认识;再通过练习巩固所学知识，加深印象。根据以上的分析和教学大纲的要求，确定了本节课的重点和难点。 二、教学目标的确定 根据教学内容的分析，将条件概率的定义、计算公式及其应用作为知识与技能目标;为渗透新的教学理念，强调了合情推理与演绎推理的过程及其重要性，既培养了学生的推理能力，又加深对公式的理解，过程中自然让学生感知从具体到抽象，从特殊到一般，从感性到理性的认知过程;此外，在计算概率问题时，因其具有不确定性，故学生容易想当然，教师要引导学生凡事要经过缜密的思考与计算方可，对学生进行辨证唯物主义教育，培养学生坚持实事求是的态度、锲而不舍的科学精神。 三、教学方法和教学手段的选择 根据新课标的要求，讲授法不能让学生更好的吸收知识，没有实现应试教育向素质教育的转型，而发现式的教学方法不仅培养了学生的观察与归纳能力，而且可以使学生更好地理解知识，讨论法的应用可以进一步促使学生发现问题，从而更好的解决问题，还能够培养其合作精神;现代的教学手段可使得问题能够更形象地展现在学生眼前，适应于学生的形象思维，体现了课堂视觉与听觉的同步性与交互性，因而选择多媒体教学。 四、教学过程的设计 为达到本节课的教学目标，突出重点，突破难点，教学上采取了以下的措施: (1)在探索概念阶段, 让学生经历从直观到抽象、从特殊到一般、从感性到理性的认知过程，完成对条件概率公式的三次认识,使得学生对概念的认识不断深入。 (2)在应用概念阶段, 让学生应用条件概率公式解决课前问题，前后呼应，感受两种方法解决问题的异同，同时培养学生坚持实事求是的态度，不可想当然。 (3)在总结概念阶段，让学生再次理解公式的含义，总结出条件概率的本质，强调合情推理与演绎推理在公式推导中的重大作用。 t pipe welding, construction workers and technicians on every road, every instrument as well recorded and well identified in of the guarantee instrument tubes as small as possible, selection of high quality, high precision sleeve connector. Instrumenquality parts replacement. Supply good quality of purchasing instrument and ovality -Department to check its overall quality, poor in order to fundamentally solve oil spill problems. Plant for local Panel after installation, in conjunction with the qualityance, to ensure that the use of electric door and actuator installation quality and equipment to the site to check its seal, accepter and more elegant. 5 thermal process control measures for quality problems 5.1 control thermal duct system leakage measure s neatt spacing between lines, flat, should be around the corner in the same location, same shape, to ensure that the wiring procesf the device line cards, the wiring from the upper to the lower, from left to right in the order. Fixed to maintain consistention oe fastened, dense, solid, clean, and beautiful. Secondary wiring the cable terminations should be arranged by the actual locacracks, break. Tinned copper nose clean solder full exterior surface is smooth without burrs. Control cable Assembly should bd, no the process, no bubbles in the thermoplastics pipes, linear nose consistent with the core wire specifications, contact is gooen cables pass through the firewall, of lax structure of local fire safety clamps. Thermoplastics production, to comply with t strength, surface appearance. Whof support and hanger. Cable hole plugging gaps should use qualified fireproof materials, block surface should have sufficien5r to review and then transported for the construction. Amount of insulation materials shallaccordance with the requested test indicator test, according to the inspection report and approved by the supervising engineees in rvision engineers arrived at the scene, after confirmation by the supervising engineer, seal immediately sent authorized bodiing quality inspection and acceptance every day to ensure that the welding ... All unreleased material sampling, invited supe, weldents for welding personnel certified, and welding before welding training, select skills good sense to carry out constructionstrument, welding welding following the end of each review, responsibility and prevention of welding, welding wrong. Requiremthe in