ralph rolls a single die two times in a row. what is the probability that he will roll a \three\ both…

ralph rolls a single die two times in a row. what is the probability that he will roll a \three\ both times?\na $\frac{1}{3}$\nb $\frac{1}{18}$\nc $\frac{1}{36}$\nd $\frac{1}{6}$

ralph rolls a single die two times in a row. what is the probability that he will roll a \three\ both times?\na $\frac{1}{3}$\nb $\frac{1}{18}$\nc $\frac{1}{36}$\nd $\frac{1}{6}$

Answer

Answer:

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

Explanation:

Step1: Probability of rolling a 3 on first roll

A die has 6 sides. The probability of rolling a 3 on the first roll is $\frac{1}{6}$ since there is 1 favorable outcome (rolling a 3) out of 6 possible outcomes.

Step2: Probability of rolling a 3 on second roll

The second - roll is an independent event. The probability of rolling a 3 on the second roll is also $\frac{1}{6}$ as the die has 6 sides and 1 side is a 3.

Step3: Probability of both events occurring

For independent events $A$ and $B$, the probability of both $A$ and $B$ occurring is $P(A\cap B)=P(A)\times P(B)$. Here, $A$ is the event of rolling a 3 on the first roll and $B$ is the event of rolling a 3 on the second roll. So $P = \frac{1}{6}\times\frac{1}{6}=\frac{1}{36}$.