Question

Two dice are thrown at the same time write down all the possible outcomes. What is the probability that the sum of the two numbers appearing on the top of the die is a prime number

Answer 1

all possible outcomes are = (1,1), (1,2), (1,3),(1,4), (1,5), (1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5), (4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,7)

p(getting sum of two no is prime no) = 15/36

= 5/12

Answer 2

The required probability is $\frac{5}{12}$.

Step-by-step explanation:

Consider the provided information.

Two dice are thrown at the same time.

The possible outcomes are:

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

Now the sum is prime:

The number of pairs are: (1,1), (1,2), (2,1), (1,4), (2,3), (3,2), (4,1), (1,6), (2,5), (3,4),(4,3), (5,2), (6,1), (6,5) (5,6)

There are 15 pairs out of 36 whose sum is a prime number.

$Probability=\frac{15}{36} =\frac{5}{12}$

Hence, the required probability is $\frac{5}{12}$.

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