Question

A newspaper has decided to launch an advertising campaign to attract new subscribers. The goals are to attract at least 1,000 new young (no more than 40 years old) subscribers and to attract at least 2,000 new older (at least 41 years old) subscribers. Suppose the probability of reaching the first goal is 0.6, the probability of reaching the second goal is 0.4, and the probability of reaching both goals is 0.15. Which of the following is true?

a. P(goal 1 is reached, goal 2 isn't) = 0.45

b. P(neither goal is reached) = 0.15

c. P(goal 2 is reached, goal 1 isn't) = 0.25

d. All of these choices are true.

Answer 1

P(First goal) = 0.6, P(Second goal) = 0.4, P(Both goals) = 0.15

We check each choice.

a)

P(Goal 1 reach, goal 2 isn't) = P(Goal 1) - P(Both goals)

= 0.6 - 0.15

= 0.45

TRUE.

b)

P(Either goal is reached) = P(goal 1) + P(goal 2) - P(both goals)

= 0.6 + 0.4 - 0.15

= 0.85

P(neither goal is reached) = 1 - P(Either goal reached)

= 1 - 0.85

= 0.15

TRUE

c)

P(Goal 2 reached , but goal 1 isn't) = P(goal 2) - P(Both goals)

= 0.4 - 0.15

= 0.25

TRUE.

ANSWER: All of these choices are true