The Solution:
Given:
(a) The probability that the next gumball is yellow is:
[tex]P(yellow)=\frac{Number\text{ of yellow}}{Total\text{ number of gumballs}}=\frac{4}{4+2+8}=\frac{4}{14}=\frac{2}{7}[/tex]
(b) The probability someone gets a
yellow gumball chews it, and then gets a second yellow gumball.
That is, without replacement.
[tex]P(YY)=P(Y_1)\times P(Y_2)=\frac{4}{14}\times\frac{3}{13}=\frac{2}{7}\times\frac{3}{13}=\frac{6}{91}[/tex]
(c) The probability a gumball is orange given that it is not yellow.
[tex]P(Orange\text{/}_{not\text{ yellow}})=\frac{\frac{8}{14}\times\frac{10}{14}}{\frac{10}{14}}=\frac{8}{14}=\frac{4}{7}[/tex]
Therefore, the correct answers are:
(a) 2/7
(b) 6/91
(c) 4/7
