Staff Inc., a management consulting company is surveying the personnel of Burger

Question

Staff Inc., a management consulting company is surveying the personnel of Burger Limited. It determined that 35% of the analysts have an MBA and that 40% of all analysts are over age 35. Further, of those who have an MBA, 30% are over age 35. a.) What is the probability that a randomly chosen analyst both has an MBA and also is over age 35? b.) What is the probability that a randomly chosen analyst who is over age 35 has an MBA? c.) What is the probability that a randomly chosen analyst has an MBA or is over age 35? d.) What is the probability that a randomly chosen analyst who is over 35 does not have an MBA? e.) Are the events MBA and over age 35 independent? Why or why not? f.) Are the events MBA and over age 35 mutually exclusive? Why or why not? g.) Are the events MBA and over age 35 collectively exhaustive? Why or why not?

Explanation / Answer

Ans:

Given that

P(MBA)=0.35

P(over 35)=0.40

P(over age/MBA)=0.30

a)

P(both MBA and over age)=P(over age/MBA)*P(MBA)=0.30*0.35=0.105

b)

P(MBA/over 35)=P(both MBA and over age)/P(over 35)

=0.105/0.40

=0.2625

c)P(MBA or over 35)=P(MBA)+P(over 35)-P(both MBA and over 35)

=0.35+0.40-0.105

=0.645

d)P(over 35 but not MBA)=P(over 35)-P(both MBA and over 35)

=0.40-0.105=0.295

e)As,P(over age/MBA) is not equal to P(over age),so not independent.

f)Not mutually exclusive,as P(both MBA and over 35) is not equal to 0.

g)No,as sum of probabilities is not 1.

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