Question

a. find the probability that when a single six - sided die is rolled, the outcome is 4.
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 27.
a. the probability of rolling a 4 on a six - sided die is \square.
(round to three decimal places as needed.)

Explanation:

Step1: Determine total outcomes

A six - sided die has 6 possible outcomes: 1, 2, 3, 4, 5, 6. So the total number of possible outcomes \(n = 6\).

Step2: Determine favorable outcomes

We want the outcome to be 4. There is only 1 favorable outcome (i.e., getting a 4), so the number of favorable outcomes \(m=1\).

Step3: Calculate probability

The formula for probability \(P\) is \(P=\frac{m}{n}\). Substituting \(m = 1\) and \(n=6\) into the formula, we get \(P=\frac{1}{6}\approx0.167\) (rounded to three decimal places).

Answer:

\(0.167\)