In a population of 100,000 women, it can be expected that 90%

Question

In a population of 100,000 women, it can be expected that 90% live up to 60 years and 60% live up to 90 years. Given that a woman in this group is 60 years old, what is the probability that she will live until 90?

A) 50%
B) 52%
C) 60%
D) 67%
E) 75%

A) 50%
B) 52%
C) 60%
D) 67%
E) 75%

gmatophobia · Answer

Let's assume that the population equals 100.

Number of individuals who are expected to live up to 60 years = 90% of 100 = 90

Number of individuals who are expected to live up to 90 years = 60% of 100 = 60

Required Probability = 60/90 = 2/3 = 0.6666

= 67%

Option D

Kinshook · Answer

Given: In a population of 100,000 women, it can be expected that 90% live up to 60 years and 60% live up to 90 years. 
Asked: Given that a woman in this group is 60 years old, what is the probability that she will live until 90?

Percentage of women who are expected to live up to 60 years = 90%
Percentage of women who are expected to live up to 90 years = 60%

Probability of a 60 year old women to live until 90 = 60%/90% = 2/3 = 66.66%

IMO D

Jatin108 · Answer

hi why do we divide the two probabilities ?

Aritrakarak · Answer

Hi, I like to imagine it this way. For a woman to live till 60 yrs, she has to be one of the 90000 women who make it (90% of 100000). Hence we can conclude there are 90000 women aged 60.
Now, if we go back in time, we see the probability of a woman making it to 90 yrs is 60%. Which means there would be 60000 women aged 90 (60% of 100000).

Now from 60 yrs to 90 yrs we see that 30000 women don't make it. Which means that the woman in question has to be one of the 60000 women who make it - out of the 90000 women who will start from the age of 60.

Hence 60000/90000 or 60%/90%

MarkGMATMentor · Answer

This is a question about a dependent probability. While mathematically simple, you must be clear on how to handle questions like these logically.
 
If the woman has lived to 60, she is already part of the 90%. In other words, there is no chance that she'll be part of the 10% that didn't live to 60.

In effect, you are now "starting over" with a new total of 90% (or 90,000 women). But the 60% was off the old total of 100% (or 100,000). And since 60 is 2/3 of 90 (or, 60,000 is 2/3 of 90,000), she has a 2/3 or approximately 67% probability of living until 90.  The answer is D.

How does this fit with dependent probability? 
The probability of a woman living to 90  given that she lives to 60  is 67%. You can confirm that since makes sense with the dependent probability formula:
Probability of B = Probability of A * Probability of B  given A 
Probability of living to 90 = Probability of living to 60 * Probability of living to 90  given living to 60  
60% = 90% * 67%

Here, we solved for:
Probability of living to 90  given living to 60  = Probability of living to 90 / Probability of living to 60
67% = 60% / 90%

This is considered a hard question, but if you can get solid on fundamental probability principles, you can answer questions like this quickly.

In a population of 100,000 women, it can be expected that 90%

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

In a population of 100,000 women, it can be expected that 90%

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards