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 2 is reached, goal 1 isn't) = 0.25

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

c. P(neither goal is reached) = 0.15

d. All of these choices are true.

Question

contestada

Respuesta :

ACCESS MORE ACCESS MORE ACCESS MORE ACCESS MORE

AyBaba7 AyBaba7 · Answer 1 · 2020-02-19T13:46:54+01:00

Answer:

Option D is correct.

All of these choices are true.

Step-by-step explanation:

Let the probability of reaching first goal be P(A)

And probability of reaching second goal be P(B)

P(A) = 0.6

P(B) = 0.4

P(A n B) = 0.15

P(A') = probability that first goal isn't reached = 1 - P(A) = 1 - 0.6 = 0.4

P(B') = probability that second goal isn't reached = 1 - P(B) = 1 - 0.4 = 0.6

P(universal set) = 1

a) Probability that goal 2 is reached, goal 1 isn't = P(A' n B)

P(B) = P(A n B) + P(A' n B)

P(A' n B) = P(B) - P(A n B) = 0.4 - 0.15 = 0.25

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

b) Probability that goal 1 is reached, goal 2 isn't = P(A n B')

P(A) = P(A n B) + P(A n B')

P(A n B') = P(A) - P(A n B) = 0.6 - 0.15 = 0.45

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

c) Probability that neither goal is reached = P(A' n B')

P(Universal set) = P(A n B') + P(A n B') + P(A n B) + P(A' n B')

1 = 0.45 + 0.25 + 0.15 + P(A' n B')

P(A' n B') = 1 - (0.45 + 0.25 + 0.15) = 1 - 0.85 = 0.15

P(neither goal is reached) = 0.15 is also correct.