Question

Six 6-sided dice are rolled. What is the probability that exactly two of the dice show a 1 and exactly two of the dice show a 2? Express your answer as a common fraction.

Answer 1

Using it's concept, the probability that exactly two of the dice show a 1 and exactly two of the dice show a 2 is: 10/243.

What is a probability?

A probability is given by the number of desired outcomes divided by the number of total outcomes.

One of the six numbers is of 1, and also one out of six is 2. The other two trials can be any of the other 4 numbers, hence the probability for the six rolls has the following format:

p = (1/6)² x (1/6)² x (4/6)²

This considers just one order, while there are six rolls, hence there are 6! possible orders, hence the probability is:

p = 6! x (1/6)² x (1/6)² x (4/6)² = 120 x 16/46656 = 10/243.

More can be learned about probabilities at https://brainly.com/question/14398287

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