Approach 1: Find the total number of combinations = 2^5=32. Find the number of combinations when Kate wins: out of 5 games, she can win 3 or 4 times only as 5 victories would put her over the $14 mark and less than 3 victories, below the $10.
The number of combinations for winning 3 times:
5C3=10
Number of combinations for winning 4 times:
5C4=5
Remember, nCk=n! / k!∗(n−k)!.
Probability equals 5+1032=1532.
Approach 2: write out the combinations:
[3] : 123, 124, 125, 134, 135, 145, 234, 235, 245, 345
[4] : 1234, 1235, 1245, 1345, 2345
Total: 1532.
The combinations can be summed because they have equal probabilities of 132 each.
The correct answer is B
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Thanks,
Prashant Ponde
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