Question

a. find the probability that when a single six - sided die is rolled, the outcome is 1. 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 19. a. the probability of rolling a 1 on a six - sided die is (round to three decimal places as needed.)

Explanation:

Step1: Identify total and favorable outcomes for die - 1 case

A six - sided die has 6 possible outcomes (1, 2, 3, 4, 5, 6). The favorable outcome (rolling a 1) is 1.
The probability formula is $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So, $P(\text{rolling a }1)=\frac{1}{6}$.

Step2: Identify total and favorable outcomes for coin - tails case

A coin toss has 2 possible outcomes (heads and tails). The favorable outcome (getting tails) is 1. So, $P(\text{tails})=\frac{1}{2}$.

Step3: Identify total and favorable outcomes for die - 19 case

A six - sided die has 6 possible outcomes (1 - 6). The number of ways to roll a 19 is 0. So, $P(\text{rolling a }19)=\frac{0}{6}=0$.

Answer:

a. $\frac{1}{6}\approx0.167$
b. $\frac{1}{2}=0.500$
c. $0.000$