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If I roll  standard -sided dice and multiply the number on the face of each die, what is the probability that the result is a composite number?

 Jan 20, 2024
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To find the probability, we'll count the successful outcomes (composite products) and divide by the total possible outcomes.

 

Total Outcomes: Rolling two 6-sided dice has 6 * 6 = 36 possible outcomes.

 

Composite Outcomes: A composite number is a number that has more than two factors (excluding 1 and itself). Let's list the products that are not composite:

 

1 * 1 = 1 (prime)

 

1 * 2 = 2 (prime)

 

1 * 3 = 3 (prime)

 

1 * 5 = 5 (prime)

 

2 * 2 = 4 (prime)

 

4 * 4 = 16 (prime)

 

5 * 5 = 25 (prime)

 

There are 7 outcomes that are not composite. Therefore, 36 - 7 = 29 outcomes are composite.

 

Probability: The probability of a composite product is 29 successful outcomes out of 36 possible outcomes, which is 29/36.

 

Therefore, the probability that the product is composite is 29/36.

 Jan 21, 2024

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