Question

to start a board game,the player who rolls two sixes gets to go first.what is the probability that a player will roll two number cubes and get two sixes?
1/36
1/18
1/12
4/15

Explanation:

Step1: Determine single - roll probability

The probability of rolling a six on a single six - sided number cube is $\frac{1}{6}$ since there is 1 favorable outcome (rolling a six) out of 6 possible outcomes (numbers 1 - 6).

Step2: Use multiplication rule for independent events

Since the rolls of the two number cubes are independent events, the probability of two independent events $A$ and $B$ both occurring is $P(A\cap B)=P(A)\times P(B)$. Here, $A$ is the event of rolling a six on the first cube and $B$ is the event of rolling a six on the second cube. So the probability of rolling two sixes is $\frac{1}{6}\times\frac{1}{6}=\frac{1}{36}$.

Answer:

A. $\frac{1}{36}$