Given:
The number of pink balls in the urn = 8.
The number of green balls in the urn = 6
The number of balls randomly drawn from the urn =5
Required:
We need to find the probability of selecting 5 balls that all are pink.
Explanation:
The balls are replaced after selection.
The sample space = the total number of balls in the urn= 8+6
[tex]n(S)=14[/tex]Let A be the event of selecting a pink ball.
The favourable outcomes = The number of pink balls = 8
[tex]n(A)=8[/tex]The probability of selecting 5 balls from an urn that all are pink,
[tex]=\frac{n(A)}{n(S)}\times\frac{n(A)}{n(S)}\times\frac{n(A)}{n(S)}\times\frac{n(A)}{n(S)}\times\frac{n(A)}{n(S)}[/tex][tex]=\frac{8}{14}\times\frac{8}{14}\times\frac{8}{14}\times\frac{8}{14}\times\frac{8}{14}[/tex][tex]=\frac{32768}{537824}[/tex][tex]=0.0609269947[/tex][tex]=0.061[/tex]Final answer:
The probability that the 5 balls will be pink is 0.061.