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Chapter 2: Q.2.19 (page 49)

Two symmetric dice have had two of their sides painted red, two painted black, one painted yellow, and the other

painted white. When this pair of dice are rolled, what is the probability that both dice land with the same color face up?

Short Answer

Expert verified

The probability that both dice land with the same color face-up is0.28.

Step by step solution

01

Given Information.

Two symmetric dice have had two of their sides painted red, two painted black, one painted yellow, and the other painted white.

02

Explanation.

The same color on face-up can be any of the 4colors. Let's find the probability of landing a color when only 1dice are rolled.

P(red)=2/6P(black)=2/6P(white)=1/6P(yellow)=1/6

Since both dice are independent of each other we can just multiply the individual values to get probabilities for the same color on the up face.

P(red)=(2/6)*(2/6)=4/36P(black)=(2/6)*(2/6)=4/36P(white)=(1/6)*(1/6)=1/36P(yellow)=(1/6)*(1/6)=1/36

P(samecolor)=P(red)+P(black)+P(white)+P(yellow)

P(Samecolour)=(4/36)+(4/36)+(1/36)+(1/36)=10/36=0.28

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