Question

Two dice are thrown at random. Find the probability of getting: (i) an even number as sum (ii) a total of at least 10 (iii) the sum as a prime number​

Answer 1

Answer:

Step-by-step explanation:

Solution:

Given in the question

Two dice are thrown at random

Number of possible outcome = 36

Solution(i)

We need to calculate probability of getting an even number as sum

Sum as even numbers are 2,4,6,8,10,12

Possible outcomes are (1,1),(1,3),(2,2),(3,1),(1,5),(2,4),(3,3),(4,2),(5,1),(2,6),(3,5),(4,4),(5,3),(6,2),(4,6),(5,5),(6,4),(6,6)

P(Even number) = 18/36 or 1/2

So there is 1/2 probability of getting an even number as sum.

Solution(ii)

We need to calculate probability a total of at least 10 i.e.

Sum of at least 10 are 10,11,12

Possible outcomes are (4,6),(5,5),(6,4),(5,6),(6,5),(6,6)

P(Sum at least 10) = 6/36 or 1/6

So there is 1/6 probability a total of at least 10.

Solution(iii)

We need to calculate probability that the sum as a prime number

Prime numbers as sum are 2,3,5,7,11

Possible outcomes 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),(5,6),(6,5)

P(Prime number) = 15/36 = 5/12

So there is 5/12 probability that the sum as a prime number.