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

Explanation:

Step1: Calculate probability of rolling a number less than 4

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

Step2: Calculate probability of getting heads on coin - toss

A fair coin has 2 possible outcomes (heads or tails). The probability of getting heads, denoted as $P(B)$, is $\frac{1}{2}$.

Step3: Use the multiplication rule for independent events

Since rolling a number - cube and tossing a coin are independent events, the probability of both events occurring, $P(A\cap B)$, is $P(A)\times P(B)$. So $P(A\cap B)=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$