Question: 2nd Ball is Yellow

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Comment on 2nd Ball is Yellow

Can we solve this problem using the complement rule?
greenlight-admin's picture

Sure, give it a try.

Hi,
I tried using complement rule, but I got 2/25 instead of 1/25, can you analyze where I went wrong?

P( having second ball yellow)= 1-P( 2nd not being yellow)
= 1-P( 2nd being either red+ 2nd being green)
= 1-(12/25 x 12/24+ 12/25 x 11/24+ 12/25 x 12/24 +12/25 x11/24)
= 1-( 12/25 + 11/25)
= 1-23/25
= 2/25 (what went wrong?)
greenlight-admin's picture

It's hard to tell, because you haven't really explained all of your steps. However, I believe you forgot to include P(1st ball is yellow and 2nd ball is ANY color)

This probability = (1/25)(24/24) = 1/25
I think this is your missing 1/25

I have a doubt here. The question asks for the probability that the second ball is yellow. Considering that the 1st ball selected is a non yellow ball, in the formula-> P(A AND B) = P(A) * P(B|A). Here isn't it true that we have to only find the probability of the last part of formula which is P(B|A)? So considering that the 1st ball selected is non yellow, then we have 24 balls remaining among which 1 is yellow, so the answer is 1/24? why is this not correct? Please explain.
greenlight-admin's picture

In order for the 2nd ball to be yellow, the 1st ball must be NON-YELLOW. So, we have to factor that into our equation.

That is, P(2nd ball yellow) = P(1st ball is not yellow AND 2nd ball is yellow)

We can't just assume that the first ball is not yellow, since there's a 1/25 chance that the first ball is yellow.

Cheers,
Brent

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