dtweah wrote:The probability of picking an apple from a basket is .25 and that of picking a rotten fruit is .50. The probability of picking a rotten apple is .14. Find the prob that neither an apple nor a rotten fruit is picked.

A. .75

B. .39

C. .25

D. .5

E. .61

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Hi!

Even if we're stumped by the math, we can immediately eliminate 3 of the 5 choices and then eliminate a 4th.

Since the probability of picking a rotten fruit is .5, even if there were no apples the probability of choosing a non-rotten fruit would be .5. Since there are apples, and not all of them are rotten, the answer must be less than .5 - eliminate A, D and e.

There's a .25 chance of picking an apple. If there were no overlap between apples and rotten, then there would be a .75 (.5 + .25) chance of picking an apple or rotten, giving us a .25 (1 - .75) chance of picking neither apple nor rotten. Since there is some overlap, there must be a greater than .25 chance of drawing rotten or apple.

So, the answer must be greater than .25 - eliminate C.

Only B remains!

Stuart Kovinsky wrote:

dtweah wrote:The probability of picking an apple from a basket is .25 and that of picking a rotten fruit is .50. The probability of picking a rotten apple is .14. Find the prob that neither an apple nor a rotten fruit is picked.

A. .75

B. .39

C. .25

D. .5

E. .61

[spoiler]https://www.greguide.com/Free-GRE-Practi ... est-5.html[/spoiler]

Hi!

Even if we're stumped by the math, we can immediately eliminate 3 of the 5 choices and then eliminate a 4th.

Since the probability of picking a rotten fruit is .5, even if there were no apples the probability of choosing a non-rotten fruit would be .5. Since there are apples, and not all of them are rotten, the answer must be less than .5 - eliminate A, D and e.

There's a .25 chance of picking an apple. If there were no overlap between apples and rotten, then there would be a .75 (.5 + .25) chance of picking an apple or rotten, giving us a .25 (1 - .75) chance of picking neither apple nor rotten. Since there is some overlap, there must be a greater than .25 chance of drawing rotten or apple.

So, the answer must be greater than .25 - eliminate C.

Only B remains!

Wonderful reasoning Stuart!!! The math is pretty is easier than it seems though.

dtweah wrote:
Wonderful reasoning Stuart!!! The math is pretty is easier than it seems though.

Well, we could have just done:

Prob(neither) = 1 - (prob at least one)

Prob(neither) = 1 - (Prob(apple) + Prob(rotten) - Prob(both))

Prob(neither) = 1 - (.25 + .5 - .14)

Prob(neither) = 1 - .61

Prob(neither) = .39

but what's the fun in that?