Question

When Alice spends the day with the babysitter, there is a 0.6 probability that she turns on the TV and watches a show. Her little sister Betty cannot turn the TV on by herself. But once the TV is on, Betty watches with probability 0.8. Tomorrow the girls spend the day with the babysitter.

(a) What is the probability that both Alice and Betty watch TV tomorrow?
(b) What is the probability that Betty watches TV tomorrow?
(c) What is the probability that only Alice watches TV tomorrow?

Answer 1

Explanation:

a) There is a 48% probability that both Alice and Betty watch TV tomorrow.

b) There is a 48% probability that Betty watches TV tomorrow.

c) There is a 12% probability that only Alice watches TV tomorrow.

Explanation:

We have these following probabilities:

A 60% probability that Alice watches TV.

If Alice watches TV, there is an 80% probability that Betty also watches TV.

(a) What is the probability that both Alice and Betty watch TV tomorrow?

With our probabilities above.

There is a 48% probability that both Alice and Betty watch TV tomorrow.

(b) What is the probability that Betty watches TV tomorrow?

Betty can only watch TV when Alice watches. So this is the same probability that both Alice and Betty watch TV tommorow, that is, 48%.

(c) What is the probability that only Alice watches TV tomorrow?

There is a 60% probability that Alice watches TV tomorrow.

If Alice watches TV, there is an 80% probability that Betty also watches TV. So, there is a 100%-80% = 20% probability that Betty does no watch TV.

So

There is a 12% probability that only Alice watches TV tomorrow

Answer 2

a) There is a 48% probability that both Alice and Betty watch TV tomorrow.

b) There is a 48% probability that Betty watches TV tomorrow.

c) There is a 12% probability that only Alice watches TV tomorrow.

Explanation:

We have these following probabilities:

A 60% probability that Alice watches TV.

If Alice watches TV, there is an 80% probability that Betty also watches TV.

(a) What is the probability that both Alice and Betty watch TV tomorrow?

With our probabilities above.

`P = 0.6*0.8 = 0.48`

There is a 48% probability that both Alice and Betty watch TV tomorrow.

(b) What is the probability that Betty watches TV tomorrow?

Betty can only watch TV when Alice watches. So this is the same probability that both Alice and Betty watch TV tommorow, that is, 48%.

(c) What is the probability that only Alice watches TV tomorrow?

There is a 60% probability that Alice watches TV tomorrow.

If Alice watches TV, there is an 80% probability that Betty also watches TV. So, there is a 100%-80% = 20% probability that Betty does no watch TV.

So

`P = 0.6*0.2 = 0.12`

There is a 12% probability that only Alice watches TV tomorrow.