Question

you roll a 6 - sided die. what is p(3 or factor of 56)? simplify your answer and write it as a fraction or whole number.

Explanation:

Step1: Identify possible outcomes on the die

A 6 - sided die has outcomes: \(1, 2, 3, 4, 5, 6\)

Step2: Find factors of 56 within die outcomes

Factors of 56 are numbers that divide 56 without a remainder. Let's check each die outcome:

• \(1\): \(56\div1 = 56\), so 1 is a factor.
• \(2\): \(56\div2 = 28\), so 2 is a factor.
• \(3\): \(56\div3\approx18.67\), not a factor.
• \(4\): \(56\div4 = 14\), so 4 is a factor.
• \(5\): \(56\div5 = 11.2\), not a factor.
• \(6\): \(56\div6\approx9.33\), not a factor.

So factors of 56 on the die are \(1, 2, 4\).

Step3: Identify the event "3 or factor of 56"

The outcomes for "3 or factor of 56" are the union of the set \(\{3\}\) and the set of factors of 56 on the die (\(\{1, 2, 4\}\)). So the combined set is \(\{1, 2, 3, 4\}\).

Step4: Calculate the probability

The probability \(P\) of an event is the number of favorable outcomes divided by the total number of possible outcomes.

Total number of possible outcomes when rolling a die is \(n = 6\).

Number of favorable outcomes (for "3 or factor of 56") is \(m=4\) (since the favorable outcomes are \(1, 2, 3, 4\)).

So \(P(3\text{ or factor of }56)=\frac{m}{n}=\frac{4}{6}=\frac{2}{3}\)

Answer:

\(\frac{2}{3}\)