1. 5.4 Multiplying Probability
Advanced Math Topics
5.4 Multiplying Probability

2. 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!

3. 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

4. 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 The probability
that his wife has a life insurance policy given that her husband has a life insurance
policy is 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%

5. 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 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%

6. HW
P. 264 #1-14