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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

SumFrequency214330442555672775870953104611281215

If the dice are thrown once more, then what is the probability of getting a sum
(i) 3?
(ii) More than 10?
(iii) Less than or equal to 5?
(iv) Between 8 and 12?

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Solution

The total number of times, two dice are thrown simultaneously, n(S) = 500.

(i) Number of times getting a sum 3, n(E)= 30
Probability of getting a sum 3 =n(E)n(S)=30500=350=0.06
Hence, the probability of getting a sum 3 is 0.06.

(ii) Number of times getting a sum more than 10, n(E1)=28+15=43
Probability of getting a sum more than 10 =n(E1)n(S)=43500=0.086
Hence, the probability of getting a sum more than 10 is 0.086.

(iii) Number of times getting a sum less than or equal to 5,
n(E2)=55+42+30+14=141
Probability of getting sum less than or equal to 5 =n(E2)n(S)=141500=0.282
Hence, the probability of getting a sum less than or equal to 5 is 0.282.

(iv) Number of times getting a sum between 8 and 12,
n(E3)=53+46+28=127
Required probability =n(E3)n(S)=127500=0.254
Hence, the probability of getting a sum between 8 and 12 is 0.254.

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