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02 Apr 2021, 07:15
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
73% (01:52) correct
27%
(01:58)
wrong
based on 66
sessions
History
Date
Time
Result
Not Attempted Yet
Private Benjamin is a member of a squad of 10 soldiers, which must volunteer 4 of its members for latrine duty. If the members of the latrine patrol are chosen randomly, what is the probability that private Benjamin will be chosen for latrine duty?
A. 1/10
B. 1/5
C. 2/5
D. 3/5
E. 4/5
A. 1/10
B. 1/5
C. 2/5
D. 3/5
E. 4/5
02 Apr 2021, 07:27
Kudos
Bookmarks
Given: Private Benjamin is a member of a squad of 10 soldiers, which must volunteer 4 of its members for latrine duty.
Asked: If the members of the latrine patrol are chosen randomly, what is the probability that private Benjamin will be chosen for latrine duty?
Total number of ways to choose 4 members out of 10 for latrine duty = 10C4
Number of ways to choose 4 members out of 10 for latrine duty when private Benjamin is also chosen = 9C3
Probability that private Benjamin will be chosen for latrine duty = 9C3/10C4 = (9*8*7/3*2*1)/(10*9*8*7/4*3*2*1) = 4/10 = 2/5
IMO C
Asked: If the members of the latrine patrol are chosen randomly, what is the probability that private Benjamin will be chosen for latrine duty?
Total number of ways to choose 4 members out of 10 for latrine duty = 10C4
Number of ways to choose 4 members out of 10 for latrine duty when private Benjamin is also chosen = 9C3
Probability that private Benjamin will be chosen for latrine duty = 9C3/10C4 = (9*8*7/3*2*1)/(10*9*8*7/4*3*2*1) = 4/10 = 2/5
IMO C
05 Apr 2021, 08:15
Kudos
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Bunuel
Direct approach:
\(\frac{C^1_1*C^3_9}{C^4_{10}}=\frac{2}{5}\).
Reverse approach:
1 - (the probability of 4-member groups without Benjamin) = \(1 -\frac{C^4_9}{C^4_{10}}=\frac{2}{5}\).
Answer: C.
