Question

A. Bree and Kendra love to go to the movies. When they go, there is a probability of 0.3 that Bree will buy popcorn. The probability that Kendra will buy popcorn is 0.35 if Bree buys popcorn and 0.65 if Bree does not. When Bree and Kendra go to the movies together, find the probability that

1. both buy popcorn;
2. neither buys popcorn;
3. exactly one of them buys popcorn;

B. Carmelita accompanies Bree and Kendra to the movies sometimes. During these trips, the probability that Carmelita buys popcorn is 0.55 if both Bree and Kendra buy popcorn and 0.4 if exactly one of Bree and Kendra buys popcorn. When Bree, Kendra, and Carmelita go to the movies together, find the probability that

4. all three buy popcorn;

5. Kendra and Carmelita buy popcorn, but Bree does not;

Answer 1

GIVEN THAT :-

A]]]]

Accoridng to the question we have that required

there is a probability of 0.3 that Bree will buy popcorn.P(A1)=0.3

The probability that Kendra will buy popcorn is 0.35 if Bree buys popcorn.P(A2/A1)=0.35

0.65 if Bree does not.P(A2/A1^c)=0.65

TO FIND :-1)the probability that both buy popcorn.

Let,

A1 = event that Bree will buy popcorn

A2 = event that Kendra will buy popcorn

Now finding the both buy popcorn=

=  

substituting the values we get that ,

= 0.35 *0.3

=0.105.   

finding the there fore substituting all the value we get

= 0.35 * 0.3 + 0.65 * (1 - 0.3)

= 0.56

so ,

the probability that both buy popcorn = P(A2)=0.56

TO FIND :-b)the probability that neither buys popcorn?

=

substituting the values we get that

1 - 0.3 - 0.56 + 0.105

= 0.245

therefore,

the probability that neither buys popcorn=0.245

TO FIND :-c)the probability that exactly one of them buys popcorn?

=

substituting all the valueas we get that

=0.65

therefore ,

the probability that exactly one of them buys popcorn= 0.65

now

B]]]

according to the question we have that ,the probability that Carmelita buys popcorn is 0.55 if both Bree and Kendra buy popcorn and 0.4 if exactly one of Bree and Kendra buys popcorn.

TO FIND :-4)find the probability that all three buy popcorn?

Let A3 = event that Carmelita will buy popcorn

= 0.55 * 0.35 * 0.3

= 0.05775

the probability that all three buy popcorn = 0.05775

TO FIND :-5)probability that Kendra and Carmelita buy popcorn, but Bree does not?

substituting the value we get that

= 0.4 * 0.65 * (1 - 0.3)

= 0.182

probability that Kendra and Carmelita buy popcorn, but Bree does not = 0.182.

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