nahid078 wrote:A bag contains 5 white marbles and 5 black marbles. If each of 5 girls and 5 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?
a) 1/126
b) 1/120
c) 1/24
d) 4/25
e) 1/2
There's a VERY long thread about this question here:
https://www.beatthegmat.com/probability- ... 28296.html
The easiest/fastest way to determine the probability is to examine the probability of each necessary outcome to guarantee that the girls (and subsequently the boys) draw the same colored marble.
So, P(all girls select same color) = P(1st girl selects
any marble
AND 2nd girl selects marble the SAME color as 1st girl
AND 3rd girl selects marble the SAME color
AND 4th girl selects marble the SAME color
AND 5th girl selects marble the SAME color
AND the boys get the rest)
= P(1st girl selects
any marble)
x P(2nd girl selects marble the same color as 1st girl)
x P(3nd girl selects marble the same color as 1st girl)
x P(4th girl selects marble the same color as 1st girl)
x P(5th girl selects marble the same color as 1st girl)
x P(the boys get the rest)
This equals: 1 x 4/9 x 3/8 x 2/7 x 1/6 x 1
= [spoiler]1/126[/spoiler]
=
A
NOTE: The 1 at the beginning of the product represents the probability that the 1st girls selects
any marble. Since this first girl can select any marble, the probability is 1 that she will accomplish this.
Cheers,
Brent
