Two dice are rolled. Find the probability of getting a 5 on either die or the sum of both dice is 5.

Two dice are rolled. Find the probability of getting a 5 on either die or the sum of both dice is 5.

N(S)= Total possibility = 36
N(E) = possibility = (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (1,5), (2,5), (3,5), (4,5), (6,5), (1,4), (2,3), (3,2), (4,1) = 15

P(E) = N(E)/N(S) = 15/36 = 5/12

Number of possible outcomes when 2 dice are rolled = 6^2 = 36
Number of outcomes favourable as detailed below = 15
Sum=5 ...(1,4) (2,3) (3,2) (4,1)
5 on either die = 6*2-1(repeated 5,5) = 11
Required probability = 15/36 = 5/12

5 as sum:
1+4
2+3
3+2
4+1

5 on either die
5+1
5+2
...etc
1+5
2+5
...etc

(6 possibilities) + (6 possiblities) - 1 repeat = 11

11+4 = 15 possibilities

Answer: 15/36