a number cube is rolled and a coin is tossed. the number cube and the coin are fair. what is the probability…

Explanation:

Step1: Find probability of rolling a number greater than 4

A number - cube has 6 faces numbered 1 - 6. The numbers greater than 4 are 5 and 6. So the probability of rolling a number greater than 4, $P(A)=\frac{2}{6}=\frac{1}{3}$.

Step2: Find probability of getting heads on coin - toss

A fair coin has 2 possible outcomes (heads or tails). So the probability of getting heads, $P(B)=\frac{1}{2}$.

Step3: Use the multiplication rule for independent events

Since rolling the cube and tossing the coin are independent events, the probability of both events occurring is $P(A\cap B)=P(A)\times P(B)$. $P(A\cap B)=\frac{1}{3}\times\frac{1}{2}=\frac{1}{6}$.

Answer:

$\frac{1}{6}$