Question

A gumball machine contains 4 yellow, 2 red, and 8 orange gumballs.Find each of the following probabilities. Enter your answer as a fraction. REDUCE ALL FRACTIONS.a) The probability the next gumball is yellow.b)The probability someone gets a yellow gumball, chews it, and then gets a second yellow gumball.c)The probability a gumball is orange given that it is not yellow.

Answer 1

The Solution:

Given:

(a) The probability that the next gumball is yellow is:

`P(yellow)=\frac{Number\text{ of yellow}}{Total\text{ number of gumballs}}=(4)/(4+2+8)=(4)/(14)=(2)/(7)`

(b) The probability someone gets a

yellow gumball chews it, and then gets a second yellow gumball.

That is, without replacement.

`P(YY)=P(Y_1)* P(Y_2)=(4)/(14)*(3)/(13)=(2)/(7)*(3)/(13)=(6)/(91)`

(c) The probability a gumball is orange given that it is not yellow.

`P(Orange\text{/}_{not\text{ yellow}})=((8)/(14)*(10)/(14))/((10)/(14))=(8)/(14)=(4)/(7)`

Therefore, the correct answers are:

(a) 2/7

(b) 6/91

(c) 4/7