Question

Two dice are thrown simultaneously. What is the probability that the sum of the two numbers come up is a prime number

Answer 1

Two dice are thrown simultaneously.

So, total number of outcomes = 6×6 = 36

(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)

We have to find the probability that the sum of the two numbers come up is a prime number.

Now, what is a prime number?

→ Which is greater than 1 and factors are 1 & itself.

Example: 2, 3, 5, 7, 11 & so on

Now, the favourable outcomes are:

2: (1,1)

3: (1,2) (2,1)

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

7: (5,2) (2,5) (1,6) (6,1) (3,4) (4,3)

11: (6,5) (5,6)

Therefore, number of favourable outcomes = 15

We know that,

Probability = Total number of outcomes/Number of favourable outcomes

Substitute the values

→ 15/36

→ 5/12

Therefore, the required probability is 5/12.

Answer 2

QUESTION:-

Two dice are thrown simultaneously. What is the probability that the sum of the two numbers come up is a prime number.

SOLUTION:-

➡ the total number of possibe outcomes in the case is 36,

➡ [(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),(4,4),(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)]

➡ out of the listed possibilities, the favorable outcomes are,

➡ [(1,1),(1,2),(1,3)(1,4),(1,6),(2,1),(2,3),(2,5),(3,2),(3,4),(4,1),(4,3),(5,2),(5,6),(6,1),(6,5)]

➡ .°. the number of favorable outcomes are 15.

NOW,

➡ probability = total number of outcomes / number of favorable outcomes .

➡ probability = 36/15

➡ .°. probability = 15/36 ( substitute the values)

➡ .°. probability = 5/12.