Assume you have applied for two jobs a and b. the probability that you get an offer for job a is 0.23. the probability of being offered job b is 0.20. the probability of getting at least one of the jobs is 0.35. a. what is the probability that you will be offered both jobs? b. are events a and b mutually exclusive? why or why not? explain.

Probabilities are used to determine the chance of an event.

The probabilities are given as:

(a) Probability that he gets both jobs

First, we calculate the probability that he gets one of the jobs

This is calculated as:

So, we have:

The probability that he gets both job is:

So, we have:

(b) Check if the events are mutually exclusive

Two events are said to be mutually exclusive if:

In other words,

Hence, the events are not mutually exclusive

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a, P(A or B) = P(A) + P(B) - P(A and B)

... 0.35 = 0.23 + 0.30 - P(A and B)

... P(A and B) = 0.43 - 0.35

... P(A and B) = 0.08

b. If events A and B are mutually exclusive, P(A and B) = 0. Here, P(A and B) ≠ 0, so the events are not mutually exclusive.

you answer is a

step-by-step explanation: