Question

A pair of dice rolled together till a sum of either 5 or 7 obtained. Find probability that 5 comes before 7

Answer 1

Hi there!
Here's the answer:

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¶ No. of total Outcomes when 2 dice are rolled = 6² = 36

• Favourable case for getting Sum 5 on the two dice are (1.4) , (2,3) , (3,2) , (4,1)

Probability of getting a Sum 5 = 4/36

• Favourable cases for sum 7 on the two dice are (1,6) , (2,5) , (3,4) , (4,3) , (5,2) , (6,1)

Now,
Calculate required probability using conditional probability

Probability of getting a sum 5 provided that the sum is either 5 or 7 is

P(sum = 5/sum = 5 or7) =
(4/36) + [(4/36) + (6/36)]
= (4/36) /[ (10/36)]
= 4/10
= 2/5

•°• Required Probability = 2/5

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Hope it helps