The probability that a student at a certain college is male is 0.498 . The probability that a student at that college has a job off campus is 0.712. The probability that a student at the college is male and has a job off campus is 0.315.
Find the following probabilities. Write your answer in decimal notation rounded to the nearest thousandth.
If a student is chosen at random from the college,
(a) the probability that the student is either male or has an off campus job is Answer?
(b) the probability that the student is neither male nor has an off campus job is Answer?
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
Negative = (1-the probability)
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To find the answer to these questions, we can use the concepts of probability and set notation. Let's go step by step.
(a) The probability that the student is either male or has an off-campus job can be calculated using the formula for the union of two events. The formula is:
P(A or B) = P(A) + P(B) - P(A and B)
In this case, let's define event A as the student being male and event B as the student having an off-campus job. We are given the probabilities P(A) = 0.498, P(B) = 0.712, and P(A and B) = 0.315.
Using the formula, we can calculate:
P(A or B) = P(A) + P(B) - P(A and B)
= 0.498 + 0.712 - 0.315
= 0.895
Therefore, the probability that the student is either male or has an off-campus job is approximately 0.895.
(b) The probability that the student is neither male nor has an off-campus job can be found by subtracting the probability that the student is male or has an off-campus job from 1. This is because the sum of the probabilities of all possible outcomes must equal 1.
Let's call event C as "the student is neither male nor has an off-campus job." We can calculate P(C) as follows:
P(C) = 1 - P(A or B)
= 1 - 0.895
= 0.105
Therefore, the probability that the student is neither male nor has an off-campus job is approximately 0.105.