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Math  /  Data & Statistics

QuestionIf two dice are rolled, what is the probability of not rolling at least one prime number? The answer must be represented as a reduced fraction. □\square Basic

Studdy Solution

STEP 1

1. Two six-sided dice are rolled.
2. The numbers on each die range from 1 to 6.
3. Prime numbers on a die are 2, 3, and 5.
4. The total number of outcomes when rolling two dice is 6×6=366 \times 6 = 36.

STEP 2

1. Identify the prime numbers on a single die.
2. Calculate the probability of rolling at least one prime number.
3. Calculate the probability of not rolling at least one prime number.
4. Express the probability as a reduced fraction.

STEP 3

Identify the prime numbers on a single die: 2, 3, 5.

STEP 4

Calculate the probability of rolling at least one prime number.
- Probability of rolling a non-prime number on one die: - Non-prime numbers are 1, 4, 6. - Probability of a non-prime number on one die: 36=12\frac{3}{6} = \frac{1}{2}.
- Probability of rolling non-prime numbers on both dice: - (12)×(12)=14\left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) = \frac{1}{4}.
- Probability of rolling at least one prime number: - 1−14=341 - \frac{1}{4} = \frac{3}{4}.

STEP 5

Calculate the probability of not rolling at least one prime number:
- This is the complement of rolling at least one prime number. - Probability of not rolling at least one prime number: 14\frac{1}{4}.

STEP 6

Express the probability as a reduced fraction:
- The probability is already in its simplest form: 14\frac{1}{4}.
The probability of not rolling at least one prime number is:
14 \boxed{\frac{1}{4}}

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