Question

sam rolls 3 standard fair dice. that probability that the three numbers rolled on the dice are the sides of a triangle is , where are relatively prime positive integers. what is the value of ?

Answer 1

The required probability for three numbers rolled on the dice are the sides of a triangle is 31/36.

What is probability?

The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability.

Here,

When three dice are rolled, there are 63=216 possible outcomes, or triplets (x, y, z).

Once more, in a triangle, any two sides added together are larger than the third side, or (x+y)>z.

As a result, 186 outcomes or triplets are possible and satisfy this property.

Hence, the required probability is 186/216=31/36.

The required probability is 31/36 for three dice rolls to produce triangle sides.

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