5.4 Multiplying Probability Advanced Math Topics 5.4 Multiplying Probability

p(A and B) = p(A) • p(B) ½ • ½ • ½ • Multiplying Independent Events Events whose probabilities are the same no matter what happens with the other event If A and B are Independent Events, then… p(A and B) = p(A) • p(B) Example: You flip two coins and roll two dice. Find the probability of flipping a heads, a tails, rolling an even and anything other than a 4. ½ • ½ • ½ • 5/6 = 5/48 The events are independent!

p(A and B) = p(A) • p(B | A) Multiplying Conditional Events Conditional Events: Events whose probabilities depend upon what happens in previous events If A and B are Conditional Events, then… p(A and B) = p(A) • p(B | A) Example: You select 2 cards from a deck of 52. You select the cards one at a time. Find p(diamond and a black ace) = p(diamond) • p(black ace | diamond) 13/52 • 2/51 = 1/4 • 2/51 = 2/204 = 1/102

p(A and B) = p(A) • p(B | A) From the HW P. 264 The probability that a married man has a life insurance policy is 0.89. The probability that his wife has a life insurance policy given that her husband has a life insurance policy is 0.54. Selecting a random couple, find the probability that both husband and wife have a life insurance policy. p(A and B) = p(A) • p(B | A) p(husband policy and wife policy) = p(husband policy) • p(wife policy | husband policy) = 0.89 • 0.54 = 48.06%

p(not working) = 1 – p(working) From the HW P. 264 13) There are three smoke detectors in a home. The probability that each is working is 0.92, 0.86, and 0.89. What is the probability that none of the detectors are working and a fire will go undetected? p(not working) = 1 – p(working) 1 – 0.92 = 0.08; 1 – 0.86 = 0.14; 1 – 0.89 = 0.11 The 3 events are independent. p(all 3 will not work) = 0.08 • 0.14 • 0.11 = 0.12%

HW P. 264 #1-14