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In a population of 100,000 males, 80% can be expected to live to age 60 and 60% can be expected to live to 80. Given that a male in this group is 60, what is the probability that he lives to 80?

Re: In a population of 100,000 males, 80% can be expected to live to age 6 [#permalink]

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15 May 2017, 05:19

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pushpitkc wrote:

Of the 100000 males, there are 80000 males who make it to age 60. Similarly, there are 60000 males who make it to age 80.

Since we are asked the probability of how many in the age of 60, make it to 80 : \(\frac{60000}{80000}*100\)= 75%(Option C)

Bunuel wrote:

In a population of 100,000 males, 80% can be expected to live to age 60 and 60% can be expected to live to 80. Given that a male in this group is 60, what is the probability that he lives to 80?

Re: In a population of 100,000 males, 80% can be expected to live to age 6 [#permalink]

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06 Jul 2017, 03:15

Bunuel wrote:

In a population of 100,000 males, 80% can be expected to live to age 60 and 60% can be expected to live to 80. Given that a male in this group is 60, what is the probability that he lives to 80?

Let me first write down the data given in the question, and for simplicity, I'm assuming tat there are 100 people.

By age 0 Alive = 100 Dead = 0

By age 60 Alive = 80 Dead = 20

By age 80 Alive = 60 Dead = 40

Now, consider the following questions and my understanding

What is the percentage of people who are already 60 will be alive at 80?

Answer = 60/80 = 75%

In how many ways can we select a person who is 60 years old and will be alive at 80?

Answer \(\frac{60C1}{80C1}\)

75%

Now my understanding of the original question

If a person is randomly selected from people who are 60, what is the probability that he will live to 80?

In this case. we have first already selected a person, now this particular person can be a part of the 60 people who will live to 80, or of the 20 people who will not. We have to calculate the possibility that this particular person is a part of the 60 people who live and not of the 20 people who don't. How do we do that? I know that I'm getting way too much confused here, but your answer to these questions will really help me understand probability 100%.

In a population of 100,000 males, 80% can be expected to live to age 60 and 60% can be expected to live to 80. Given that a male in this group is 60, what is the probability that he lives to 80?

Let me first write down the data given in the question, and for simplicity, I'm assuming tat there are 100 people.

By age 0 Alive = 100 Dead = 0

By age 60 Alive = 80 Dead = 20

By age 80 Alive = 60 Dead = 40

Now, consider the following questions and my understanding

What is the percentage of people who are already 60 will be alive at 80?

Answer = 60/80 = 75%

In how many ways can we select a person who is 60 years old and will be alive at 80?

Answer \(\frac{60C1}{80C1}\)

75%

Now my understanding of the original question

If a person is randomly selected from people who are 60, what is the probability that he will live to 80?

In this case. we have first already selected a person, now this particular person can be a part of the 60 people who will live to 80, or of the 20 people who will not. We have to calculate the possibility that this particular person is a part of the 60 people who live and not of the 20 people who don't. How do we do that? I know that I'm getting way too much confused here, but your answer to these questions will really help me understand probability 100%.

Thanks

Hi Shashank,

You have clearly understood the Q correctly even while answering and rewording the Q. Now you pick up a person A who is part of gang of 80 person reaching 60years. Now he can get into 60 person who do reach 80 years.. So probability is 60/80.. And this is exactly you have mentioned earlier
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In a population of 100,000 males, 80% can be expected to live to age 60 and 60% can be expected to live to 80. Given that a male in this group is 60, what is the probability that he lives to 80?

A. 48% B. 60% C. 75% D. 78% E. 80%

Since 80% and 60% are expected to live to ages 60 and 80, respectively, 80,000 and 60,000 males are expected to live to ages 60 and 80, respectively. Thus, the probability that a male lives to age 80, given that he is 60, is:

60,000/80,000 = 3/4 = 75%

Answer: C
_________________

Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

Re: In a population of 100,000 males, 80% can be expected to live to age 6 [#permalink]

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11 Sep 2017, 14:28

JeffTargetTestPrep wrote:

Bunuel wrote:

In a population of 100,000 males, 80% can be expected to live to age 60 and 60% can be expected to live to 80. Given that a male in this group is 60, what is the probability that he lives to 80?

A. 48% B. 60% C. 75% D. 78% E. 80%

Since 80% and 60% are expected to live to ages 60 and 80, respectively, 80,000 and 60,000 males are expected to live to ages 60 and 80, respectively. Thus, the probability that a male lives to age 80, given that he is 60, is:

60,000/80,000 = 3/4 = 75%

Answer: C

what if he wasnt 60. what if he was 30, would the probability change?
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