An engineering school reports that 55% of its students were male (M), 40% of its students were between the ages of 18 and 20 (A), and that 25% were both male and between the ages of 18 and 20.What is the probability of a random student being a female who is not between the ages of 18 and 20? 0.27 0.25 0.30 0.45
Question
An engineering school reports that 55% of its students were male (M), 40% of its students were between the ages of 18 and 20 (A), and that 25% were both male and between the ages of 18 and 20.What is the probability of a random student being a female who is not between the ages of 18 and 20? 0.27 0.25 0.30 0.45
Solution
To solve this problem, we first need to understand the probabilities given:
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The probability of a student being male (M) is 55% or 0.55. Therefore, the probability of a student being female (F) is 1 - 0.55 = 0.45 or 45% because the total probability must add up to 1 or 100%.
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The probability of a student being between the ages of 18 and 20 (A) is 40% or 0.40. Therefore, the probability of a student not being between the ages of 18 and 20 (not A) is 1 - 0.40 = 0.60 or 60%.
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The probability of a student being both male and between the ages of 18 and 20 (M and A) is 25% or 0.25.
We are asked to find the probability of a student being a female who is not between the ages of 18 and 20 (F and not A).
Since the events of being female and not being between the ages of 18 and 20 are independent, we can simply multiply their probabilities to get the answer.
So, the probability of a student being a female who is not between the ages of 18 and 20 is 0.45 * 0.60 = 0.27 or 27%.
Therefore, the correct answer is 0.27.
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