Probability 3 Question 31

31. A pair of fair dice is rolled together till a sum of either 5 or 7 is obtained. Then, the probability that 5 comes before 7 , is… .

(1989, 2M)

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Solution:

  1. 5 can be thrown in 4 ways and 7 can be thrown in 6 ways, hence number of ways of throwing neither 5 nor 7 is 36(4+6)=26

Probability of throwing a five in a single throw with a pair of dice =436=19 and probability of throwing neither 5 nor 7=2636=1318

Hence, required probability

=19+131819+1318219+=1911318=25



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