Question

In a certain board game, a player rolls two fair six-sided dice until the player rolls doubles (where the value on each die is the same). The probability of rolling doubles with one roll of two fair six-sided dice is 1/6. What is the probability that it takes three rolls until the player rolls doubles?

A. (1/6)³
B. (5/6)³
C. (1/6)(5/6)³
D. (1/6)(5/6)²
E. (5/6)*(1/6)²

Answer 1

To calculate the probability of getting doubles on exactly the third roll in a board game, we use the sequence of (5/6)*(5/6)*(1/6) which simplifies to (1/6)(5/6)², yielding choice D as the correct answer.

Step-by-step explanation:

The question asks about the probability that it takes exactly three rolls to roll doubles with two fair six-sided dice in a board game. The probability of rolling doubles on one roll is 1/6, while the probability of not rolling doubles (rolling a non-double) is 5/6. To find the probability that it takes exactly three rolls to get doubles, the player must roll non-doubles on the first two rolls and doubles on the third roll. Therefore, we multiply the probabilities of these independent events: (5/6) for the first roll, (5/6) for the second roll, and (1/6) for the third roll.

The calculation is as follows: (5/6)×(5/6)×(1/6), which simplifies to (1/6)(5/6)². So the correct answer is choice D: (1/6)(5/6)².