Question

. Two unbiased dice are thrown. Find the probability that neither a doublet nor a total
of 10 will appear.
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Answer 1

Answer:

When two dice are throw, then Total outcome = 36

A doublet: {(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)}

Favourable outcome = 6

Sum is 10: {(4,6),(5,5),(6,4)}

Favourable outcome = 3

Again, A doublet and sum is 10: (5, 5)

Favourable outcome = 1

Now, P(either dublet or a sum of 10 appears) = P(A dublet appear) + P(sum is 10) - P(A dublet appear and sum is 10)

=> P(either dublet or a sum of 10 appears) = 6/36 + 3/36 - 1/36

                                                         = (6 + 3 - 1)/36

                                                         = 8/36

                                                         = 2/9

So, P(neither dublet nor a sum of 10 appears) = 1 - 2/9 = 7/9

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answer from examfear