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
To solve this probability problem, we need to use conditional probability. We want to find the probability that a person taking the survey is male "given" that they preferred a European automobile.
Let's break down the given information:
- Out of 188 people who prefer European cars, 112 are males.
- A total of 452 individuals were surveyed, out of which 216 were male.
To find the probability, we will use the formula:
P(Male | European) = P(Male and European) / P(European)
We already know that P(European) is 188 out of 452 survey participants:
P(European) = 188/452
Now, we need to calculate P(Male and European). This is the number of males who prefer European cars divided by the total number of survey participants:
P(Male and European) = 112/452
Finally, we can substitute these values into the formula to find the probability of being male given that one prefers a European automobile:
P(Male | European) = (112/452) / (188/452)
Simplifying this expression, we get:
P(Male | European) = 112/188
Reducing the fraction gives us the answer:
P(Male | European) = 4/143
Therefore, the probability that a person taking the survey is male given that they preferred a European automobile is 4/143.