Question

Miss Berk has 8 pairs of pajama pants and 3 pairs of slippers. Three pairs of the pajama pants are Harry Potter themed and one pair of slippers is Harry Potter themed. When she selects what she will wear to 'school' on Tuesday, what is the probability that both items will be Harry Potter themed?

Answer 1

Answer: 12

Step-by-step explanation:

Answer 2

The probability that both items will be Harry Potter themed is 1/8.

Step-by-step explanation:

Total Number of pajama pants n(P) =8

Total number of slippers n(S)= 3

Number of Harry Potter themed Pajama pants n(H.P)=3

Number of Harry Potter themed slippers n(H.S)=1

We have to determine the probability of selecting pants and slippers that are both Harry Potter themed.

If two events A and B are independent, then the probability of A and B is given by

P(A and B)=P(A)*P(B)

Here the events selecting Harry potter themed pants and selecting harry Potter themed slippers are independent.

$P(Harry\ Potter\ pants)=\frac{n(H.P)}{n(P)}$

                                       $=\frac{3}{8}$

$P(Harry\ Potter\ slippers)=\frac{n(H.S)}{n(S)} \\ =1/3$

$P(Harry\ Potter\ pants\ and\ Harry\ Potter\ slippers)=P(Harry Potter pants)\times P(Harry potter slippers)$

$=\frac{3}{8}\times \frac{1}{3} =\frac{1}{8}$

Hence probability of selecting Harry potter themed pants and Harry potter themed slippers is 1/8