Answers
From given information we have
P(3.5 GPA or higher) = 0.7
P(job offer ) = 0.6
P(3.5 GPA or higher and job offer) = 0.5
Since P(3.5 GPA or higher and job offer) is not equal to zero so events “Jack graduates with a 3.5 GPA or higher” and “Jack receives a job offer in his field “ are not mutually exclusive.
Now,
P(3.5 GPA or higher)*P(job offer ) = 0.7 *0.6 = 0.42
Since P(3.5 GPA or higher and job offer) is not equal to P(3.5 GPA or higher)*P(job offer ) so two events “Jack graduates with a 3.5 GPA or higher” and “Jack receives a job offer in his field “ are not independent.
Hence, correct option is
(b) The two events “Jack graduates with a 3.5 GPA or higher” and “Jack receives a job offer in his field “ are neither independent nor mutually exclusive
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