a coin and a number cube with the numbers 1 through 6 are tossed. what is the probability of the coin…

Explanation:

Step1: Find coin - tails probability

The probability of a coin showing tails is $\frac{1}{2}$ since there are 2 possible outcomes (heads or tails) and 1 favorable outcome (tails).

Step2: Find cube - 3 probability

The probability of a number cube showing 3 is $\frac{1}{6}$ since there are 6 possible outcomes (numbers 1 - 6) and 1 favorable outcome (the number 3).

Step3: Use multiplication rule for independent events

Since the coin - toss and the cube - roll are independent events, the probability of both events occurring is the product of their individual probabilities. So $P(\text{tails and 3})=\frac{1}{2}\times\frac{1}{6}=\frac{1}{12}$.

Answer:

$\frac{1}{12}$