help solving a probability problem: probability that a person taking a survey is male "given" that he preferred a European automobile if 112 males prefer european autos out of 188, and 216 of a total of 452 individuals were surveyed were male.
Additional information:
85 of survey participants preferred american cars (58 male, 27 female), and 179 preferred asian models (46 male, 133 female).
Answer is said to be 4/143 and I am racking my brain to figure out how.
Any assistance would be greatly appreciated!
Thank you,
Mary
Sure, I can help you solve this probability problem. To find the probability that a person taking the survey is male given that he preferred a European automobile, we need to use conditional probability.
Let's define two events:
A: The person is male.
B: The person preferred a European automobile.
We want to find P(A|B), which is the probability of event A occurring given that event B has occurred.
From the given information, we know that:
- The total number of individuals surveyed, n(S), is 452.
- The number of males who preferred European autos, n(A∩B), is 112.
- The total number of individuals who preferred European autos, n(B), is 188.
- The number of males surveyed, n(A), is 216.
Using these numbers, we can calculate P(A|B):
P(A|B) = P(A∩B) / P(B)
P(A∩B) is the probability that a person is both male and preferred a European automobile. In this case, it is 112/452 since there were 112 males who preferred European autos out of 452 individuals surveyed.
P(B) is the probability that a person preferred a European automobile. In this case, it is 188/452 since there were 188 individuals who preferred European autos out of 452 individuals surveyed.
P(A|B) = (112/452) / (188/452)
Now, simplify the expression:
P(A|B) = (112/452) * (452/188)
= 112 / 188
This simplifies to
P(A|B) = 4/143
Therefore, the probability that a person taking the survey is male given that he preferred a European automobile is 4/143.
I hope this explanation helps you understand how to solve this probability problem. Let me know if you have any further questions!