Chapter 13.3, Problem 10CFU

To determine

To find: The odds of all three kittens only 1 have stripes.

Answer to Problem 10CFU

The odds of all three kittens only 1 have stripes is $\frac{12}{23}$ .

Explanation of Solution

The number of kitten is litter are $7$ .

The number of kitten that have stripes are $4$ .

The probability of the successful outcome of an event is given by,

  $P\left(s\right)=\frac{s}{s+f}$

The probability of selection 3 kittens with only 1 having stripe is calculated as,

  $\begin{array}{c}P\left(\text{s}\right)=\frac{C\left(4,1\right)\cdot C\left(3,2\right)}{C\left(7,3\right)}\\ =\frac{\frac{4!}{\left(4-1\right)!\left(1!\right)}\times \frac{3!}{\left(3-2\right)!\left(2!\right)}}{\frac{7!}{\left(7-3\right)!\left(3!\right)}}\\ =\frac{12}{35}\end{array}$

The probability of failure is calculated as,

  $\begin{array}{c}P\left(f\right)=1-P\left(s\right)\\ =1-\frac{12}{35}\\ =\frac{23}{35}\end{array}$

The odds of all three kittens only 1have stripes is calculated as,

  $\begin{array}{c}\text{Odds}=\frac{P\left(s\right)}{P\left(f\right)}\\ =\frac{12/35}{23/35}\\ =\frac{12}{23}\end{array}$

Therefore, the odds of all three kittens only 1 have stripes is $\frac{12}{23}$ .