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.

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sqdancefan sqdancefan · Answer 1 · 2018-08-23T21:50:34+02:00

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.

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MrRoyal MrRoyal · Answer 2 · 2021-09-28T13:10:21+02:00

Probabilities are used to determine the chance of an event.

The probabilities are given as:

[tex]P(A) = 0.23[/tex]

[tex]P(B) = 0.20[/tex]

[tex]P(At\ least\ one) = 0.35[/tex]

(a) Probability that he gets both jobs

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

This is calculated as:

[tex]Pr(One) = P(A) \times P(B') + P(A') \times P(B)[/tex]

So, we have:

[tex]Pr(One) = 0.23 \times (1 - 0.20) + (1 - 0.23) \times 0.20[/tex]

[tex]Pr(One) = 0.338[/tex]

The probability that he gets both job is:

[tex]P(Both) = P(At\ least\ one) - P(One)[/tex]

So, we have:

[tex]P(Both) = 0.35 - 0.338[/tex]

[tex]P(Both) = 0.012[/tex]

(b) Check if the events are mutually exclusive

Two events are said to be mutually exclusive if:

[tex]P(A\ and\ B) = 0[/tex]

In other words,

[tex]P(Both) = 0[/tex]

Hence, the events are not mutually exclusive