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Pam and Robin each roll a pair of fair, six-sided dice. What is the probability that Pam and Robin will both roll the

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by BTGmoderatorDC » Sun May 14, 2023 5:02 pm

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Pam and Robin each roll a pair of fair, six-sided dice. What is the probability that Pam and Robin will both roll the same set of two numbers?

A. 1/216

B. 1/36

C. 5/108

D. 11/216

E. 1/18


OA D

Source: Veritas Prep
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Re: Pam and Robin each roll a pair of fair, six-sided dice. What is the probability that Pam and Robin will both roll th

by swerve » Sun Jun 25, 2023 6:27 am
BTGmoderatorDC wrote: ↑
Sun May 14, 2023 5:02 pm
 Pam and Robin each roll a pair of fair, six-sided dice. What is the probability that Pam and Robin will both roll the same set of two numbers?

A. 1/216

B. 1/36

C. 5/108

D. 11/216

E. 1/18


OA D

Source: Veritas Prep
There are \(2\) cases:

1. Both dices show the same number, so it's \(6\) out of \(36\). Then for the other player the probability to roll the same number is \(1/6 \times 1/6\).

2. There are \(30\) out of \(36\) options for the dices to be different numbers. The probability for the other player to roll the same is \(2/6 \times 1/6\).

Probability \(= 1/6 \times 1/6 \times 1/6 + 5/6 \times 2/6 \times 1/6 = 11/216\)

Therefore, D
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