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D
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A team of 2 is to be selected from a group of 5. if the number of males in the group is n, then what's the value of n?
(1) The number of males in the group is one more than the number of females
(2) The probability the team consists of at least one male is 9/10
(1) The number of males in the group is one more than the number of females
(2) The probability the team consists of at least one male is 9/10
19 Jan 2022, 06:32
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1) Only way this is possible with 5 people is if there are 3 men and 2 woman.
\(n = 3\)
SUFFICIENT
2) If the probability for the team to have at least one man is \(\frac{9}{10}\), then the probability of selecting only women is \(\frac{1}{10}\)
Let the number of women in the group be x.
\(\frac{x}{5}*\frac{x-1}{4} = \frac{1}{10}\)
\(\frac{x^2-x}{20} = \frac{2}{20}\)
\(x^2 - x = 2\)
\(x^ - x - 2 = 0\)
\((x - 2)(x + 1)\)
x = 2 or x = -1
As x cannot be negative, x = 2. If there are 2 women in a group of 5 people, then 3 are men.
\(n = 3\)
SUFFICIENT
Answer D
\(n = 3\)
SUFFICIENT
2) If the probability for the team to have at least one man is \(\frac{9}{10}\), then the probability of selecting only women is \(\frac{1}{10}\)
Let the number of women in the group be x.
\(\frac{x}{5}*\frac{x-1}{4} = \frac{1}{10}\)
\(\frac{x^2-x}{20} = \frac{2}{20}\)
\(x^2 - x = 2\)
\(x^ - x - 2 = 0\)
\((x - 2)(x + 1)\)
x = 2 or x = -1
As x cannot be negative, x = 2. If there are 2 women in a group of 5 people, then 3 are men.
\(n = 3\)
SUFFICIENT
Answer D
16 May 2023, 15:56
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Bunuel
Statement 1 is straight forward
it gives us a relation between males and females
if there are n males then there are 5-n females
we are given that n = 5-n + 1
therefore, n = 3
Sufficient.
Statement 2
The probability that the team consists of at least one male = 1 - the probability that the team consists of no male,
which is equal to
P(at least one male) = \(1 - [(5-n)C2 / 5C2] = 9/10\) (No male means choosing both team members from the set of females.)
If we calculate this, we will get n = 3
We don't have to calculate it though, we can confidently say that this statement is also sufficient.
Therefore answer - D
