Two dice are thrown simultaneously. What is the probability that the s

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

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

Answer»

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.