Bunuel wrote:

A jar has 10 marbles, a mix of red and white. Two marbles are randomly chosen from the jar. If b is the probability that both will be red, is b > 1/3?

(1) Less than 1/2 of the marbles in the jar are white.

(2) The probability that 1 white marble and 1 red marble will be chosen together is 7/15.

Kudos for a correct solution.

Need to Check if b > 1/3.

St 1: Less than 1/2 marbles are white

Possible Options are

W R

4 6 => Calculating the prob => 6/10 * 5/9 = 1/3(equal to 1/3).... No

3 7 => Calculating the prob => 7/10 * 6/9 = 7/15 (> 1/3)..... Yes

2 8

1 9

Hence this statement is not sufficient.

St 2:

Given the prob that 1 white and 1 red ball chosen is 7/15

i.e r/10 * w/9 * 2! = 7/15

Solving, rw = 21. we know r+w =10, solving r = 3, 7.

If r = 3, b = 3/10 * 2/9 = 1/15 (<1/3)

If r = 7, b = 7/15 (>1/3)

Hence Not sufficient.

Combining the two statements:

There is only one possibility: R = 7, W = 3 marbles. Here, b = 7/15(>1/3). Hence Sufficient.

Option C. Please let me know if there is some shortcut.