Probablity Problem

Question

Comments

is ans 1/3 ?

Answer 1

Let P(R) = Rotten eggs and P(G) = Good eggs.

P(R) = 3/7 , P(G1)=4/7 .P(G2)=3/6. 

$P\left (\frac{G2}{G1} \right ) = P\left (\frac{G2\cap G1}{G1}\right ) = $ 4/7 * 3/6 / 4/7 = 3/6

Ans is 1/2.

Comments

@ prabhanjan_1  why are you selecting one by one when the question has said that both eggs are taken together.

why didn't we do like this P(G2/G1)

P(G2$\cap$G1)= $_{2}^{4}\textrm{C}$/$_{2}^{7}\textrm{C}$

P(G1)=( $_{2}^{4}\textrm{C}$ +$_{1}^{3}\textrm{C}$.$_{1}^{4}\textrm{C}$ ) / $_{2}^{7}\textrm{C}$

this will give 1/3.

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Ok taking like that you will get

P(G1) = Drawing a good egg = 4C1 / 7C1 = 4/7 --- 1

 

P(G2∩G1)= Drawing two good eggs = 4C2 / 7C2 = 2/7.---2

So, (2) / (1) =>  2/7 / 4/7 = 1/2.

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The probablity is 1/3

{good, good}, {good, bad}, {bad,good}

Only 1st qualifies. So, 1/3.

Answer 2

see total 7 eggs. of which 4 are good and 3 rotten. now given 2 eggs are taken out together in which one is good. so obvious that good one must have been taken from 4 eggs which are good.
so now remains only 3 good eggs and 3 rotten eggs. now the question is asking what is the probability of 2nd egg to be good.
clearly, it is 3/6=1/2=0.5