Question

Two unbiased dice are rolled. find the probability that the sum of the number on the two face is either divisible by 5 or divisible by 6.​

Answer 1

Answer:

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Probability of an event = Number of outcomes favourable to that event/ Number of all possible outcomes.

The set of all possible outcomes is called the sample space and is denoted by S.

When two dice are tossed, the possible outcomes are (1,1),(1,2),(1,3),(1,4),(1,5),(1,6), (2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6). Hence n(S) = 36.

But we want the desired event E that the sum of numbers should nither be a multiple of 2 nor a multiple of 3. Such outcomes (1,4),(1,6),(2,3),(2,5),(3,2),(3,4),(4,1),(4,3),(5,2) (5,6),(6,1) and (6,5). We have 11 desired outcomes. So n(E) = 12.

Hence the probability of getting sum of the scores which is neither a multiple of 2 nor a multiple of 3 = n(E)/ n(S) = 12/36 = 1/3.