One person is to be selected at random

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: The number of males in the group who were born in 1960 or later Quantity B: 4 Quantity A is greater., Quantity B is greater., The two quantities are equal., The relationship cannot be determined from the information given.

6 Explanations

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Francisco Olivas

My confusion was at the second part; I made the mistake to take the 28% out of 11 rather than from 25. It is tricky to realize that the 28% is out of total population (25) not out of the number of males (11). Thank you Chris and all the others.

Oct 10, 2017 • Comment

Jonathan , Magoosh Tutor

Hi! Yes, we must take 28% of the total population of 25. I am glad it is clear now. You are welcome :)

Oct 30, 2017 • Reply

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Robert Paul

I simply subtracted 0.44 (probability of all males) by 0.28 (probability of males born before 1960) to get 0.16 (probability of all males born AFTER 1960). Then simply multiplied 0.16 (All males born after 1960) and 25 (amount of people) to get 4.

0.44 - 0.28 = 0.16

0.16 * 25 = 4

Sep 18, 2014 • Comment

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Imon Banerjee

Another way of thinking about prash's question might be, from the perspective of Probability. Probability = Success/Outcome.

P(Males born before 1960) = No. of males born before 1960/Total no. of people in the group

Here the probability of finding the Males before 1960 is given as 0.28. The number of people is 25, we have to find the No of males born before 1960.
Hence we multiply by 25 and not 11.

Aug 23, 2014 • Comment

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sughan pandita

Thanks Chris:)

Aug 20, 2014 • Comment

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prash k

Hi Chris,

for the 2nd step in this question -- why do you multiply the 0.28 by the total number of the group (which includes male + female) RATHER than 0.28 * the total number of males (which we calculated to be 11 - as per step 1).

I get lost there....

Jul 22, 2013 • Comment

Hi Prash,

I think I can help with this.

We multiply 0.28 by the total number of people in the group and not the men in the group because 0.28 already represents the men in the group. That might be confusing. Let's say it another way.

Read the information in the prompt closely: 0.28 represents "a MALE who was born before 1960." That means that 28% of 25 people are male and were born before 196—two parameters.

If 0.28 only represented people born after 1960, and we were asked to find the males born before 1960, then we would follow the approach that you described (0.28 * the total number of males). But as it is, we only have to multiply 28% of the total group.

Does this make sense? I hope so!

Jul 23, 2013 • Reply

Francisco Olivas

Thank you Kevin. That's why we also do not multiply 28% times 44% times 25 to obtain the number of males who were born in 1960 or later, right? Regards.

Oct 10, 2017 • Reply

Jonathan , Magoosh Tutor

Right. The number of males born in 1960 or later are 44% - 28% = 16% of the total population of 25. So we could also just take .16 * 25 = 4 to get the number of males born 1960 or later.

Oct 30, 2017 • Reply

Rebecca Wu

If 0.28 represents "a male AND who was born before 1960." Does this mean we multiple P(male)*P(born before 1960s) = 0.28? Thank you!

Nov 17, 2019 • Reply

Adam

Hey Rebecca!
The rule that AND = multiply only works for independent events. For dependent events, we have to use the generalized "and" rule, which is P(A and B) = P(A)*P(B|A), where P(B|A) means "B given A." In this case, then, we would have to know the probability of choosing a male, and then the probability of choosing someone born before the 1960s, given that we've already chosen a male (that is, the probability of choosing someone born before the 1960s out of only the males). Logically, we don't care about how many of the females were born before 1960. So that's why the probability of being born before 1960 in the whole group isn't relevant for us.
Hope that helps!

Nov 23, 2019 • Reply

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Chris Lele