I found this problem on the internet while trying to find

Question

I found this problem on the internet while trying to find some practice material: 

Tom has 30 apples, 15 of them are bad.Steve has 30 oranges and 6 of them are bad. Both Tom and Steve have to put two apples and two oranges in a basket at random. What is the probability that the basket would have exactly two bad apples and two bad oranges? 

I tried to solve it but looks like something is missing..........can someone help.

yuefei · Answer

P(T bad apples) = 2/15
P(S bad oranges) = 2/6

P = (2/15)*(2/6) = 4/90 = 2/45

johnbaker · Answer

But don't you have to consider the probability of picking BAD one's only from the entire lot ?

young_gun · Answer

i'm getting 4/29, but I fear I'm wrong.

KillerSquirrel · Answer

15/30*14/29 + 6/30*5/29 = 7/29 + 1/29 = 8/29 this is wrong - see followup posts

abiswas · Answer

I got 8/29 too like KS

yuefei · Answer

Why do we add the probability of these two events? These are two mutually exclusive events, and we are looking for the probability of 1 event AND the other event.

KillerSquirrel · Answer

AND ---> multiply

yuefei · Answer

Well if you throw a dice twice, what is the probability that you throw six both times?
P = (1/6)*(1/6) = 1/36

What if the question had asked what is the probability of selecting 2 bad apples or 2 bad oranges? The result would have two scenarios, which would provide for p = p(1) + p(2). Thoughts?

young_gun · Answer

this is also tripping me up!

KillerSquirrel · Answer

probability of selecting 2 bad apples or 2 bad oranges ? 21/60*14/59 ---> two bad apples 21/60*5/59 ---> two bad oranges total 21/60*14/59+21/60*5/59 =

yuefei · Answer

KillerS, you're a machine!!

KillerSquirrel · Answer

Does anyone has an OA here ? Or is this an academic debate ? :wink:

ggarr · Answer

OA here. I was thinking the answer is 7/841 (7/29*1/29)

Fig · Answer

To me

o p(2 bad apples) = 15*14 / (30*29) = 7/29 o p(2 bad oranges) = 6*5 / (30*29) = 1/29 Then, o P(2 bad orange & 2 bad apples) = p(2 bad apples) * p(2 bad oranges) = 7/29 * 1/29 = 7/(29)^2

IrinaOK · Answer

agree with calculations 7/29 x 1/29 = 7/29^2, but the result seems too low...

Fig · Answer

Well... it's 1 chance on 120 to have this specific set

... I think it's fine, the number of bad orange is low too

If the number of bad oranges were also equal to the good one, a set like this would have 1 chance on 17 to be...

KillerSquirrel · Answer

Yes - perfect as always - the answer should be 7/(29^2)

Fig · Answer

Thanks

... U are not that bad too

.... Did u fix a date for your test?

KillerSquirrel · Answer

My test will be ~ December

I found this problem on the internet while trying to find

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