9. A pair of fair dice are thrown in a gambling problem. Person A wins if...

Question

Question

9. A pair of fair dice are thrown in a gambling problem. Person A wins if the sum of numbers showing up is six or less and on

Answer 1

Answer #1

solution:

The outcome of rolling a pair of fair dice are

1 | L.1) 2 | 2.1) (31) (41) (5.1) 16 | 6.1) 2 | 1.2 [[2.2) | 3.2) | 4.2) 5.2] | 6.2) | (13) (23) | 3.3] | 4.3) [53] | 6.3) |4

Total outcomes = 36

A)

Now, A wins if the sum of numbers showing up is 6 or less and one of the die shows 4, so this makes (1,4), (4,1), (2,4), (4,2). Hence

probability that A wins = 4/36 = 1/9

B)

B wins if the sum of numbers showing up is 5 or more and one of the die shows 4, so this makes all the bold outcomes in the table.

(15) | 1.1) | 2.1) | 3.1) (4,1) | 12 | 2.2) | 3.2) (13) | 2.3) | 1.4) | (24) | 3.4) (33) (16) (2.6) | 3.6) (4,6) (56) 4,2) (4

Probability of B winning = 11/36

C)

Both A and B win when the out comes are (1,4), (4,1), (2,4),(4,2) i.e When A wins. Hence

The probability that both A and B wins = 1/9

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Answer 2

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