solution:
The outcome of rolling a pair of fair dice are
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.
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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