Problem Solving

A basket contains 5 apples of which 1 is spoiled and the rest are good. If Henry is to select 2 apples from the basket simultaneously and at random, what is the probability that 2 apples selected will include the spoiled apple?

a.1/5 b.3/10 c.2/5 d.1/2 e.3/5

Two apples are drawn simultaneously, so order does not matter (both are picked at one time).
There is 1 spoiled apple, 1 good apple, total = 2
Possible outcomes = 5
Probability = 2/5

beat_gmat_09 wrote:Two apples are drawn simultaneously, so order does not matter (both are picked at one time).
There is 1 spoiled apple, 1 good apple, total = 2
Possible outcomes = 5
Probability = 2/5

it should be 2/5 or 40%

Hey guys,

Just one point that may be worth a chime-in on these "simultaneous" probability problems. I think a lot of times the word "simultaneous" throws people off, but when you think about it there's no such thing as perfectly "simultaneous" if you take it all the way down to a nanosecond level, right? At some point your finger touches one apple before the other. So you can solve something like this methodically by using both sequences:

Spoiled, then Not Spoiled (1/5 * 4/4)

Not Spoiled, then Spoiled (4/5 * 1/4)

And then adding them together (4/20 + 4/20 = 8/20 = 2/5)

Or you can think through logically: If he picks 2 and each has a 1/5 chance of being "the spoiled one", then he has two 1/5 chances of a spoiled apple, or a 2/5 total chance.


Just thought it was worth pointing out...the word "simultaneous" in these problems carries a lot more intimidation than it's really worth...