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.
[tex]P(Harry\ Potter\ pants)=\frac{n(H.P)}{n(P)}[/tex]
[tex]=\frac{3}{8}[/tex]
[tex]P(Harry\ Potter\ slippers)=\frac{n(H.S)}{n(S)} \\ =1/3[/tex]
[tex]P(Harry\ Potter\ pants\ and\ Harry\ Potter\ slippers)=P(Harry Potter pants)\times P(Harry potter slippers)[/tex]
[tex]=\frac{3}{8}\times \frac{1}{3} =\frac{1}{8}[/tex]
Hence probability of selecting Harry potter themed pants and Harry potter themed slippers is 1/8
