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10 Aug 2023, 19:04
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Difficulty:
35%
(medium)
Question Stats:
72% (02:00) correct
28%
(02:07)
wrong
based on 57
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Ten contestants including two friends Mark and Andrew took part in a skiing competition. First five contestants would receive an IKEA gift voucher worth $250. Find the probability that Mark will win an IKEA gift voucher but Andrew will not.
(A) 1/2
(B) 5/18
(C) 1/5
(D) 2/9
(E) 5/9
(A) 1/2
(B) 5/18
(C) 1/5
(D) 2/9
(E) 5/9
10 Aug 2023, 20:44
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Total outcomes: 10c5.
And for this case, if we fix one place for Mark, we still need to choose 4 people without andrew, to do that we can use 8c4.
Probability for case when Mark wins but not Andrew is 8c4/10c5 = 5/18
And for this case, if we fix one place for Mark, we still need to choose 4 people without andrew, to do that we can use 8c4.
Probability for case when Mark wins but not Andrew is 8c4/10c5 = 5/18
11 Aug 2023, 06:36
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Probability that Mark is in the first 5 places:
5/10 = 1/2
Probability that Andrew is in the bottom 5 spots of the remaining 9:
5/9
Total Probability:
1/2 × 5/9 = 5/18
Posted from my mobile device
5/10 = 1/2
Probability that Andrew is in the bottom 5 spots of the remaining 9:
5/9
Total Probability:
1/2 × 5/9 = 5/18
Posted from my mobile device
