Two dice are rolled once. Find the probability of getting 1. both wit

1.	Two dice are rolled once. Find the probability of getting 1. both with number 5 2. first die with no. 3. sum on both the dice is 7 4. sum is 10 or more 5. both with same no.
Answer» n = 6² = 36 1. m = both with no. 5 = (5, 5) = 1 P(both 5) = m/n = 1/36 2. m = first dice with no. 1 : (1, 1) (1, 2) (1, 3) ………(1, 6) = 6 P(First die with no. 1) = 3/36 = 1/6 3. m = sum is 7 : (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) = 6 P(sum is 7) = 6/36 = 1/6 4. m = sum is 10 or more : sum (10) or (11) or (12) (4, 6), (5, 5), (6, 4) + (6, 5), (5, 6) + (6, 6) = 6 P(sum is 10 or more) = 6/36 = 1/6 5. m = Both with same number: (1, 1) (2, 2) (3, 3) P(both dice with same no.) = 6/36 = 1/6.

Two dice are rolled once. Find the probability of getting 1. both with number 5 2. first die with no. 3. sum on both the dice is 7 4. sum is 10 or more 5. both with same no.

Answer»

n = 6² = 36

1. m = both with no. 5 = (5, 5) = 1

P(both 5) = m/n = 1/36

2. m = first dice with no. 1 : (1, 1) (1, 2) (1, 3) ………(1, 6) = 6

P(First die with no. 1) = 3/36 = 1/6

3. m = sum is 7 : (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) = 6

P(sum is 7) = 6/36 = 1/6

4. m = sum is 10 or more : sum (10) or (11) or (12)

(4, 6), (5, 5), (6, 4) + (6, 5), (5, 6) + (6, 6) = 6

P(sum is 10 or more) = 6/36 = 1/6

5. m = Both with same number: (1, 1) (2, 2) (3, 3)

P(both dice with same no.) = 6/36 = 1/6.