4. Probability
Multiplication Rule: Dependent Events
Struggling with Statistics?
Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
About 15% of people in a town have both a cat and a dog. As 64% of residents have a dog, what is the probability that someone in the town owns a cat, given they have a dog?
A
0.23
B
0.15
C
0.64
D
0.096
Verified step by step guidance1
Step 1: Recognize that this is a conditional probability problem. The formula for conditional probability is P(A|B) = P(A ∩ B) / P(B), where P(A|B) is the probability of event A given event B, P(A ∩ B) is the probability of both events A and B occurring, and P(B) is the probability of event B.
Step 2: Define the events in the problem. Let A represent the event 'a person owns a cat' and B represent the event 'a person owns a dog.' The problem provides P(A ∩ B) = 0.15 (probability of owning both a cat and a dog) and P(B) = 0.64 (probability of owning a dog).
Step 3: Substitute the given values into the conditional probability formula. Using P(A|B) = P(A ∩ B) / P(B), substitute P(A ∩ B) = 0.15 and P(B) = 0.64.
Step 4: Simplify the fraction to calculate P(A|B). This will give the probability that someone owns a cat, given that they own a dog.
Step 5: Interpret the result. The final value represents the likelihood of a person owning a cat if it is already known that they own a dog.
3:47mWatch next
Master Multiplication Rule: Dependent Events with a bite sized video explanation from Patrick
Start learning
