Question

a. find the probability that when a single six - sided die is rolled, the outcome is 3. b. find the probability that when a coin is tossed, the result is tails. c. find the probability that when a six - sided die is rolled, the outcome is 24. a. the probability of rolling a 3 on a six - sided die is (round to three decimal places as needed.)

Explanation:

Step1: Recall probability formula

The probability formula is $P(E)=\frac{n(E)}{n(S)}$, where $n(E)$ is the number of favorable outcomes and $n(S)$ is the total number of possible outcomes.

Step2: Calculate for rolling a 3 on a die

For a six - sided die, $n(S) = 6$ (the possible outcomes are 1, 2, 3, 4, 5, 6) and $n(E)=1$ (only one 3). So $P(3)=\frac{1}{6}\approx0.167$.

Step3: Calculate for getting tails on a coin toss

For a coin toss, $n(S) = 2$ (heads and tails) and $n(E)=1$ (tails). So $P(\text{tails})=\frac{1}{2}=0.5$.

Step4: Calculate for rolling a 24 on a die

For a six - sided die, $n(S) = 6$ and $n(E)=0$ (since 24 is not a possible outcome on a six - sided die). So $P(24)=\frac{0}{6}=0$.

Answer:

a. 0.167
b. 0.5
c. 0