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 male or between the ages of 18 and 20? 0.22 0.25 0.70 0.95
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 male or between the ages of 18 and 20? 0.22 0.25 0.70 0.95
Solution
The probability of a student being male or between the ages of 18 and 20 can be calculated using the formula for the union of two events: P(A U B) = P(A) + P(B) - P(A ∩ B).
Here, event A is the event that a student is male, and event B is the event that a student is between the ages of 18 and 20.
Given in the problem, P(A) = 0.55, P(B) = 0.40, and P(A ∩ B) = 0.25.
Substituting these values into the formula gives:
P(A U B) = P(A) + P(B) - P(A ∩ B) = 0.55 + 0.40 - 0.25 = 0.70.
So, the probability of a student being male or between the ages of 18 and 20 is 0.70.
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