Question

Two dice are rolled and product of the outcomes (numbers are found. What is the probability that the product so found is a prime numbers

Answer 1

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Answer 2

The probability of getting a prime as product would be 1/6

When two dice are rolled, their maximum product can be 36 and minimum product can be 1

The total possible cases of products are 6*6 =  36 .

The prime numbers between 1-36 are

2,3,5,7,11,13,17,19,23,29,31

A prime number is a number having only two factors : 1 and the number itself

Hence all these numbers would only be formed when one of the die rolls a 1

So, the probable cases are:

1,1         2,1        3,1          4,1         5,1          6,1        1,2         1,3    1,4      1,5     1,6

These would lead a products of: 1,2,3,4,5,6

Out of this only 2,3,5 are prime

hence favourable cases are : 6

So, the probability of getting a prime as product would be:

6/36 = 1/6