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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.

A Gumball Machine Contains 4 Yellow 2 Red And 8 Orange GumballsFind Each Of The Following Probabilities Enter Your Answer As A Fraction REDUCE ALL FRACTIONSa Th class=

Sagot :

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

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