Question

Two dice are thrown simultaneously 500 times. Each time the sum of two numbers appearing on their tops is noted and recorded as given in the following table:

Sum	Frequency
2	14
3	30
4	42
5	55
6	72
7	75
8	70
9	53
10	46
11	28
12	15

If the dice are thrown once more, what is the probability of getting a sum

1. 3?
2. more than 10?
3. less than or equal to 5?
4. between 8 and 12?

Answer 1

Total number of times, when two dice are thrown simultaneously, n(S) = 500

i. Number of times of getting a sum 3,

n(E) = 30

∴ Probability of getting a sum 3 = `(n(E))/(n(S))`

= `30/500`

= `3/50`

= 0.06

Hence, the probability of getting a sum 3 is 0.06

ii. Number of times of getting a sum more than 10,

n(E₁) = 28 + 15 = 43

∴ Probability of getting sum more than 10 = `(n(E_1))/(n(S))`

= `43/500`

= 0.086

Hence, the probability of getting a sum more than 10 is 0.086

iii. Number of times of getting a sum less than or equal to 5,

n(E₂) = 55 + 42 + 30 + 14 = 141

∴ Probability of getting a sum less than or equal to 5 = `(n(E_2))/(n(S))`

= `141/500`

= 0.282

Hence, the probability of getting a sum less than or equal to 5 is 0.282.

iv. The number of times of getting a sum between 8 and 12,

n(E₃) = 53 + 46 + 28 = 127

∴ Required probability = `(n(E_3))/(n(S))`

= `127/500`

= 0.254

Hence, the probability of getting a sum between 8 and 12 is 0.254.