mathew rolls a number cube labeled with the numbers 1 - 6. he then flips a fair coin. what is the…

Explanation:

Step1: Calculate roll - 4 probability

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

Step2: Calculate flip - head probability

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 rolling the die and flipping 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:

$\frac{1}{12}$