Probability Question

Question

Hi All, I got the below question while doing a CAT using GMATPrep: A basket of fruit contains 5 apples, of which 1 is rotten and the rest are good. Harry selects 2 apples from the basket simultaneously and at random. What is the probability that the 2 apples selected will include the rotten apple? I got this wrong, and the answer implied that there was replacement of one apple before picking the next, but the word "simultaneously" surely means that replacement is not allowed? Any help on this one is appreciated! Out of interest - does anyone know what % of the Quant GMAT questions are likely to be ones similar to the above, involving probability & combinations? Thanks in advance!

mkpoway · Answer

The probability will be

# ways to pick 2 apples that include 1 bad apple / total # ways to pick 2 apples

For the numerator, you could pick the bad apple plus any of the other 4 apples, so 1*4 = 4.

For the denominator, it will be the sum of the numbers of ways to pick 2 good apples, plus the number of ways to pick 1 bad and 1 good apple. The number of ways to pick 2 good apples will be 4*3 or 12.

Therefore I get 4/16 = 1/4.

sidhu4u · Answer

I think this is how I would've done it:
=> probability that 2 apples selected will include the rotten apple = 1 - probability that both are good apples
=> probability that both are good apples (without replacement) = 4/5 * 3/4 = 3/5
Therefore probability that 2 apples selected will include the rotten apple = 1 - 3/5 = 2/5

You can also do it this way:
Answer = (1C1 * 4C1)/5C2 = 2/5
Here 1C1 = number of ways of choosing 1 rotten apple
4C1 = number of ways of choosing 1 good apple from 4 good apples
5C2 = number of ways of choosing 2 apples from 5

What was the given answer?

vscid · Answer

4C1 / 5C2 = 2/5

What is the OA?

sudgmat · Answer

Hi mkpoway

Just want to explain you something. 
 
To find the number of ways to choose 2 good apples, Choosing Apple-A and then Apple-B (both good apples) is same as choosing Apple -B then Apple-A. so we have to do combination not permutation.

so it will be 4C2 =  \frac{4*3}{2} = 6 (you had 12 in your answer)
so Total number of ways = 6 + 4 =10

Probability Question

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