In a bag, there are total 30 gemstones. Out of which 8 are rubies, 10 are sapphires and the rest
are emeralds. What is the probability of picking out a stone randomly which is neither emerald nor
sapphire?
Answers
Answer:
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GMAT Club Forum Index Problem Solving (PS)
A certain bag of gemstones is composed of two-thirds : Problem Solving (PS)
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BG
May 29, 2006
00:00ABCDE
DIFFICULTY: 65% (hard) QUESTION STATS: based on 338 sessions
64% (02:50) correct
36% (02:44) wrong
A certain bag of gemstones is composed of two-thirds diamonds and one-third rubies. If the probability of randomly selecting two diamonds from the bag, without replacement, is 5/12, what is the probability of selecting two rubies from the bag, without replacement?
(A) 5/36
(B) 5/24
(C) 1/12
(D) 1/6
(E) 1/4
Spoiler: OA
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Most Helpful Expert Reply
VeritasKarishma
EXPERT'S
POST
Jan 9, 2014
b00gigi wrote:
Can someone explain the
2/3 * (2R-1)/(3R-1)
part?
Say, a bag has 6 diamonds and 3 rubies. What is the probability of selecting 2 diamonds one after the other without replacement?
Probability of selecting one diamond = 6/9
Probability of selecting yet another diamond after selecting one = 5/8 (no of diamonds has gone down by 1 and total no. of diamonds has gone down by 1 too)
Total probability = (6/9)*(5/8)
Here, we assume that no of rubies is R and no of diamonds is 2R (since no of diamonds is twice the no of rubies)
Probability of selecting two diamonds without replacement = (2R/3R) * (2R - 1)/(3R - 1) = 5/12
Either cross multiply to get the value of R or try to plug in some values to see where you get a multiple of 12 in the denominator.
Once you get the value of R as 3, you know the number of diamonds is 6.
Probability of picking two rubies one after the other without replacement = (3/9) *(2/8) = 1/12
Answer:
0 possiblity because there are only gemstones there not random stones...