Question

practice finding probabilities of compound events. mathew rolls a number cube labeled with the numbers 1 - 6. he then flips a fair coin. what is the probability that he rolls a 4 and flips a head? write your answer as a fraction.

Explanation:

Step1: Find probability of rolling a 4

The probability of rolling a 4 on a 6 - sided number cube is $\frac{1}{6}$ since there is 1 favorable outcome (rolling a 4) out of 6 possible outcomes.

Step2: Find probability of flipping a head

The probability of flipping a head on a fair coin is $\frac{1}{2}$ since there is 1 favorable outcome (head) out of 2 possible outcomes (head or tail).

Step3: Use multiplication rule for independent events

Since the roll of the cube and the flip of the coin are independent events, the probability of both events occurring is the product of their individual probabilities. So $P(\text{roll 4 and flip head})=\frac{1}{6}\times\frac{1}{2}$.
$P(\text{roll 4 and flip head})=\frac{1\times1}{6\times2}=\frac{1}{12}$

Answer:

$\frac{1}{12}$