experts help plz

[quantskillsgmat]

Q two identical urns-black and white each contain 5 blue,5 red and 10 green balls.every ball selected from black urn is immediately returned to the urn,while each ball selected from white urn is removed and placed on a table.If jenny receives a quarter for every blue ball,a dime for every red ball and a nickel for every green ball she selects.what is probability that she will be able to buy a 25 cent candy bar with the proceeds from drawing four balls two from each urn.
a)143/152 b)14/37 c)1 d)0 e)2/3

[Snowbirds]

The only scenario where Jenny can't purchase the candy bar is if she selects 4 green balls. Therefore, overall probability is 1-P(4 green balls)

From the black urn:
1/2 * 1/2 = 1/4

From the white urn:
1/2 * 9/19 = 9/38

Combining together (1/4)*(9/38) = 9/152

1-9/152 = 143/152

a

[factor26]

Very nice post snowbird - it is also important to stress here that we should be multiplying the undesired outcomes (prob of 2 green from black * prob of 2 green from white) as the only way to not afford a candy bar in this situation is by drawing 2 green from one urn AND 2 green from the other. Additing them would indicate both situations are possible in obtaining our result.