Question

An urn contains nine blue balls and seven yellow balls. If three balls are selected randomly without being​ replaced, what is the probability that of the balls​ selected, one of them will be blue and two of them will be​ yellow?

Answer 1

`Probability = (27)/(80)`

Explanation:

Given

`Blue =9`

`Yellow = 7`

Required

Determine the probability that one of the balls is blue while others is yellow

The order of selection may be any of these three:

Yellow, Yellow, Blue or Yellow, Blue, Yellow or Blue, Yellow, Yellow

Solving Yellow, Yellow, Blue

`Probability = P(Y_1) * P(Y_2) * P(B)`

`Probability = (7)/(16) * (6)/(15) * (9)/(14)`

`Probability = (1)/(8) * (1)/(5) * (9)/(2)`

`Probability = (9)/(80)`

Solving Yellow, Blue, Yellow

`Probability = P(Y_1) * P(B) * P(Y_2)`

`Probability = (7)/(16) * (9)/(15) * (6)/(14)`

`Probability = (9)/(80)`

Solving Blue, Yellow, Yellow

`Probability = P(B) *P(Y_1) * P(Y_2)`

`Probability = (9)/(16) * (7)/(15) * (6)/(14)`

`Probability = (9)/(80)`

Hence:

The required probability is:

`Probability = (9)/(80) + (9)/(80) + (9)/(80)`

`Probability = (27)/(80)`