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 25.

a. the probability of rolling a 3 on a six - sided die is \\(\square\\).
(round to three decimal places as needed.)

b. the probability of a result of tails when tossing a coin is \\(\square\\).
(round to three decimal places as needed.)

c. the probability of rolling a 25 on a six - sided die is \\(\square\\).
(round to three decimal places as needed.)

Explanation:

Part a

Step1: Identify possible outcomes

A six - sided die has 6 possible outcomes: 1, 2, 3, 4, 5, 6.

Step2: Identify favorable outcomes

The favorable outcome (rolling a 3) is 1.

Step3: Calculate probability

The formula for probability $P(E)=\frac{\text{Number of favorable outcomes}}{\text{Number of possible outcomes}}$. So $P(\text{rolling a }3)=\frac{1}{6}\approx0.167$.

Part b

Step1: Identify possible outcomes

When a coin is tossed, there are 2 possible outcomes: heads and tails.

Step2: Identify favorable outcomes

The favorable outcome (getting tails) is 1.

Step3: Calculate probability

Using the probability formula $P(E)=\frac{\text{Number of favorable outcomes}}{\text{Number of possible outcomes}}$, we get $P(\text{tails})=\frac{1}{2} = 0.500$.

Part c

Step1: Identify possible outcomes

A six - sided die has outcomes from 1 to 6, so there are 6 possible outcomes.

Step2: Identify favorable outcomes

It is impossible to roll a 25 on a six - sided die, so the number of favorable outcomes is 0.

Step3: Calculate probability

Using the probability formula $P(E)=\frac{\text{Number of favorable outcomes}}{\text{Number of possible outcomes}}$, we get $P(\text{rolling a }25)=\frac{0}{6}=0.000$.

Answer:

s:
a. $\frac{1}{6}\approx0.167$
b. $\frac{1}{2} = 0.500$
c. $\frac{0}{6}=0.000$