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Out of a group of 10 contestants, 2 are to be selected at random. What 06 Jun 2016, 04:14
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Out of a group of 10 contestants, 2 are to be selected at random. What is the maximum number of male contestants possible if the probability that both selected contestants are male is less than 10% ?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
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D
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Out of a group of 10 contestants, 2 are to be selected at random. What 06 Jun 2016, 07:12
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Let n be the number of man. Probability = n/10 * (n-1)/9= n(n-1)/90.
For the probability to be less than 10%, n(n-1) < 9.
Maximum number that satisfies this condition is 3. For 4, it is > 9. Hence the answer is D.
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Out of a group of 10 contestants, 2 are to be selected at random. What 07 Jun 2016, 11:44
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Bunuel
Out of a group of 10 contestants, 2 are to be selected at random. What is the maximum number of male contestants possible if the probability that both selected contestants are male is less than 10% ?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
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Let x be the number of males.
Total contestants = 10

Probability that the first contestant selected is a male = x/10
Probability that the second contestant selected is also a male = x-1/9

Total probability = x(x-1)/ 90 < 1/10 (this probability is less than 10%)

Solving for x we get, x(x-1)< 9. This implies that the maximum value of x can be 3.

Answer D!
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Out of a group of 10 contestants, 2 are to be selected at random. What 27 Dec 2020, 10:54
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Bunuel
Out of a group of 10 contestants, 2 are to be selected at random. What is the maximum number of male contestants possible if the probability that both selected contestants are male is less than 10% ?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Show more

1. Suppose there are \(M\) males and \(F\) females

2. The probability of choosing both contestants as male will be \(\frac{M}{10} * \frac{M-1}{10-1}\) or Desired Outcome / Total Outcomes

2.a. As a side note, because we cannot have the same person on both the spots, hence we apply the minus one in the above expression. In other words, once a person is chosen, he/she will not be available for the next spot

3. Now, we are given that this probability is less than \(10%\)

4. \(\frac{M}{10} * \frac{M-1}{9} < \frac{1}{10}\) --> \(M(M-1) < 9\)

5. As the answer options are in increasing order and we are asked to find the max. lets start from option E

6. If \(M = 4\) then \(M(M-1) = 12\) which is not less than \(9\)

5. If \(M = 3\) then \(M(M-1) = 6\) which is less than \(9\)

Ans. D
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Out of a group of 10 contestants, 2 are to be selected at random. What 08 Aug 2025, 13:48
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