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One person is to be selected at random from a group of 25 pe

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One person is to be selected at random from a group of 25 pe [#permalink] New post 22 Nov 2017, 10:15
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One person is to be selected at random from a group of 25 people. The probability that the selected person will be a male is 0.44, and the probability that the selected person will be a male who was born before 1960 is 0.28.

Quantity A
Quantity B
The number of males in the group who were born in 1960 or later
4


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: One person is to be selected at random from a group of 25 pe [#permalink] New post 22 Nov 2017, 16:16
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Now we have total number of people \(= 25\).

Now number of men in the group \(= 25 \times 0.44 = 11\). Since probability of selecting men \(= 0.44 =\frac{11}{25}\).

Similarly number of men born before 1960 \(= 25 \times 0.28 =7\).

The number of males in the group who were born in 1960 or later \(= 11-7=4\).

Hence option C is correct!
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Re: One person is to be selected at random from a group of 25 pe [#permalink] New post 07 May 2018, 07:30
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Carcass wrote:
One person is to be selected at random from a group of 25 people. The probability that the selected person will be a male is 0.44, and the probability that the selected person will be a male who was born before 1960 is 0.28.

Quantity A
Quantity B
The number of males in the group who were born in 1960 or later
4


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


Let M = number of males in the group (among 25 people)

The probability that the selected person will be a male is 0.44
So, we can write: M/25 = 0.44
ASIDE: We can solve this equation for M in several ways. My approach is to rewrite 0.44 as a fraction
We get: M/25 = 44/100
Simplify right side to get: M/25 = 11/25
At this point, we can see that M = 11
In other words, there are 11 males in the group of 25 people


The probability that the selected person will be a male who was born before 1960 is 0.28
Let B = number of people in the group who are BOTH male and born before 1960

So, we can write: B/25 = 0.28
We get: B/25 = 28/100
Simplify right side to get: B/25 = 7/25
At this point, we can see that B = 7
In other words, there are 7 people who are BOTH male and born before 1960

RECAP: There are 11 males in the group of 25 people. Among those 11 males, 7 were born BEFORE 1960
So, the other 4 males must have been born AFTER 1960

So, we get:
Quantity A: 4
Quantity B: 4

Answer: C

Cheers,
Brent
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Re: One person is to be selected at random from a group of 25 pe   [#permalink] 07 May 2018, 07:30
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