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06:31According to Bayes’ Theorem, the probability of event A , given that event B has occurred, is
P(A|B) = P(A) * P(B|A)P(A) * P(B|A) + P(A') * P(B|A').
In Exercises 33–38, use Bayes’ Theorem to find P(A|B).
33. P(A) = 2/3, P(A') = 1/3, P(B|A) = 1/5 , and P(B|A') = 1/2
Using a Tree Diagram In Exercises 67-70, a probability experiment consists of rolling a six-sided die and spinning the spinner shown at the left. The spinner is equally likely to land on each color. Use a tree diagram to find the probability of the event. Then explain whether the event can be considered unusual.
68. Event B: rolling an odd number and the spinner landing on green
"True or False? In Exercises 5 and 6, determine whether the statement is true or false. If it is false, rewrite it as a true statement.
5. If two events are independent, then P(A|B) = P(B)."
Finding Classical Probabilities In Exercises 41-46, a probability experiment consists of rolling a 12-sided die numbered 1 to 12. Find the probability of the event.
43. Event C: rolling a number greater than 4
Cards In Exercises 59-62, you are dealt a hand of five cards from a standard deck of 52 playing cards.
59. Find the probability of being dealt two clubs and one of each of the other three suits.
"According to Bayes’ Theorem, the probability of event A , given that event B has occurred, is
P(A|B) = P(A) * P(B|A)P(A) * P(B|A) + P(A') * P(B|A').
In Exercises 33–38, use Bayes’ Theorem to find P(A|B).
36. P(A) = 0.62, P(A') = 0.38, P(B|A) = 0.41 , and P(B|A') = 0.17 "
