3.2 Conditional Probabilities 83 BAYES'FORMULA 3.4 INDEPENDENT EVENTS EXAMPLE 2a(page 67) A student is taking a one-hour-time-limit makeup examination. Suppose the probability that the student will finish the exam in less than x hours is x/2,for all 0<x 1.Given that the student is still working after 0.75 hours,what is the conditional probability that the full hour is used 口t5:43，手，300 Xiaohan Yang Chapter 3 Conditional Probability and Independence
logo 3.2 Conditional Probabilities 3.3 BAYES’ FORMULA 3.4 INDEPENDENT EVENTS EXAMPLE 2a(page 67) A student is taking a one-hour-time-limit makeup examination. Suppose the probability that the student will finish the exam in less than x hours is x/2, for all 0 ≤ x ≤ 1.Given that the student is still working after 0.75 hours, what is the conditional probability that the full hour is used ? Xiaohan Yang Chapter 3 Conditional Probability and Independence
3.2 Conditional Probabilities 3AY5●有A 3.4 INDEPENDENT EVENTS Example In a 2-children family,Sample space =(b,b),(b.g).(g,b).(g.g). A=one of them is a boy, B=another is a boy. Find the conditional probability of B given A. Xiaohan Yang Chapter 3 Conditional Probability and Independence
logo 3.2 Conditional Probabilities 3.3 BAYES’ FORMULA 3.4 INDEPENDENT EVENTS Example In a 2-children family,Sample space =(b,b),(b,g),(g,b),(g,g), A=one of them is a boy, B=another is a boy. Find the conditional probability of B given A. Xiaohan Yang Chapter 3 Conditional Probability and Independence
3.2 Conditional Probabilities 3.3 BAYES'FORMULA 3.4 INDEPENDENT EVENTS Example From a deck of 52 cards a card is withdrawn at random and not replaced.A second card is then drawn.Find the probability that the first card is an ace and the second a king? 口t5:43，手，300 Xiaohan Yang Chapter 3 Conditional Probability and Independence
logo 3.2 Conditional Probabilities 3.3 BAYES’ FORMULA 3.4 INDEPENDENT EVENTS Example From a deck of 52 cards a card is withdrawn at random and not replaced. A second card is then drawn. Find the probability that the first card is an ace and the second a king ? Xiaohan Yang Chapter 3 Conditional Probability and Independence
3.2 Conditional Probabilities 3AY5●有A 3.4 INDEPENDENT EVENTS Example Draw two balls in turn from an urn containing 3 red balls and 5 white balls.Find the probability that the two balls drawn are red. (a)if the first ball drawn is put back in the urn; (b)if the first ball drawn is not put back. Xiaohan Yang Chapter 3 Conditional Probability and Independence
logo 3.2 Conditional Probabilities 3.3 BAYES’ FORMULA 3.4 INDEPENDENT EVENTS Example Draw two balls in turn from an urn containing 3 red balls and 5 white balls. Find the probability that the two balls drawn are red. (a) if the first ball drawn is put back in the urn ; (b) if the first ball drawn is not put back. Xiaohan Yang Chapter 3 Conditional Probability and Independence