There are 37 balls in basket A, and the probability of

Question

22. There are 37 balls in basket A, and the probability of picking a blue ball from basket A is 10.86%. Basket B has x balls and the probability of picking a blue ball from basket B is 66.67%. In basket C, there are 32 balls and the chance of picking a blue ball from basket C is 50:50.

When picking a ball from the above baskets, the probability of getting a blue ball is 1/3. What is x ?

(There are no answer choices available for this question)

cool_jonny009 · Answer

....completely lost .....

ywilfred · Answer

p = favourable / total

pA(blue) = b/37 = 10.86% -> b = 4 balls
pB(blue) = b/x = 66.67% -> b = 0.6667x (!b = x-0.6667x)
pC(blue) = b/32 = 50.5% -> 16 balls

p(!blue in A) = 100 - 10.86 = 89.14 = 0.8914
p(!blue in B) = 100 - 66.67 = 33.33 = 0.3333
p(!blue in C) = 100 - 50.50 = 49.5 = 0.495

p(!not blue) = 1 - 0.8914*0.3333*0.495 = 0.852 = 33/37 * x-0.6667x * 16/32

1.91 = x(0.3333)
x = 5.7 ~ 6 balls

gamjatang · Answer

The OA is 9.

paddy// could you explain more in detail, please?

paddy · Answer

No. of blue balls in basket A = (10.86 * 37)/100 = 4 No. of blue balls in basket B = (66.67*x)/100 No. of blue balls in basket C = 16 {4+ +16} / (37+x+32) = 1/3 ==> {20 + } / (69+x) = 1/3 ==> 3 * {20 + } = 69+x ==> 60+2x = 69+x ==>x=9

There are 37 balls in basket A, and the probability of

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards