Question

Two fair dice are rolled. What is the probability that their sum is greater than 4?​

Answer 1

Given :-

Two fair dice are rolled

To find :-

The probability that their sum is greater than 4

Solution :-

Given that

Number of dice are rolled = (n) = 2

We know that

If n dice are thrown once then the total number of all possible outcomes = 6^n

The total number of all possible outcomes = 6²

= 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)

The favourable outcomes for the sum on the both dice is greater than 4 are (1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(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)

Number of favourable outcomes = 30

We know that

Probability of an event E is P(E) = Number of favourable outcomes/ Total number of all possible outcomes

=> Probability of getting the sum is greater than 4 on both dice = 30/36 = 5/6

Answer :-

→ Probability of getting the sum is greater than 4 on both dice = 5/6

Used Formulae:-

♦ If n dice are thrown once then the total number of all possible outcomes = 6^n

♦ Probability of an event E is P(E) = Number of favourable outcomes/ Total number of all possible outcomes