Question

The probability that Jack graduates with a 3.5 GPA or higher is .7. The probability that Jack receives a job offer in his field is .6. The probability that Jack graduates with a GPA of 3.5 or higher and receives an offer in his field is .5. Which of the following is true?

	a.	The two events “Jack graduates with a 3.5 GPA or higher” and “Jack receives a job offer in his field “ are mutually exclusive
	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
	c.	The two events “Jack graduates with a 3.5 GPA or higher” and “Jack receives a job offer in his field “ are independent

Answer 1

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