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05:54According 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
"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).
35. P(A) = 0.25, P(A') = 0.75, P(B|A) = 0.3 , and P(B|A') = 0.5 "
1. When two events are mutually exclusive, why is P(A and B) = 0?
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
Classifying Events Based on Studies In Exercises 15-18, identify the two events described in the study. Do the results indicate that the events are independent or dependent? Explain your reasoning.
17. A study found that there is no relationship between playing violent video games and aggressive or bullying behavior in teenagers. (Source: The Royal Society Publishing)
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.
