a coin is tossed and a number cube is rolled. find the probability, p(heads and 7).

Explanation:

Step1: Determine coin - toss probability

A coin has 2 sides. Probability of getting heads, $P(H)=\frac{1}{2}$.

Step2: Determine number - cube roll probability

A standard number cube has 6 sides numbered from 1 to 6. The probability of rolling a 7 is $P(7) = 0$ since 7 is not on the cube.

Step3: Use multiplication rule for independent events

For independent events A and B, $P(A\cap B)=P(A)\times P(B)$. Here, $A$ is getting heads and $B$ is rolling a 7. So $P(\text{heads and }7)=P(H)\times P(7)$. Substitute values: $P(\text{heads and }7)=\frac{1}{2}\times0 = 0$.

Answer:

0