PS Probability

[samirpandeyit62]

1st draw 3 marbles can be selcted out of 9 in 9C3 = 84 ways

now here only prime nos are 2,3,5,7 rest of the 5 nos are not prime

so amongst these 84 combinations, the combinations which have exactly 1 prime are 4*5C2 = 40

so probabilty is 40/84 = 10/21

now probabilty that prme is selected while placing a ball in the cup is 1/3

so combined probabilty is 10/21 * 1/3 = 10/63

for next draw we can select 3 out of 6 in 6c3 = 20 ways

& we need 2 primes this time

so 2 primes out of 3 can be selected in 3 ways

& the other nos should be non prime i.e it can be selected out of the left 3 non prime nos in 3 ways

so together it is 3*3 =9 ways

so probabailty is 9/20

now probability that 2 primes are selected to place in the cup is 1/3

so combined P = 9/20 *1/3 = 3/20

last draw 3 balls out of 3 P=1

now probability that 1 prime is selected to put in the cup is 1/3

so combined Probability is 1*1/3 =1/3

so the reqd Probabilty is

10/63 * 3/20 * 1/3 = 1/126

Ans should be A

[ldoolitt]

1st draw 3 marbles can be selcted out of 9 in 9C3 = 84 ways

now here only prime nos are 2,3,5,7 rest of the 5 nos are not prime

so amongst these 84 combinations, the combinations which have exactly 1 prime are 4*5C2 = 40

so probabilty is 40/84 = 10/21

Agreed but a part of the explanation lacks a little bit of clarity. Since the jar has 4 primes and the final cup must have 4 primes, you cannot throw any primes away: you have to pick EXACTLY one prime in the three balls on the first draw. Thus the total number of good picks is {picking a prime for one AND picking a non prime for two}.

There are 4 ways to pick a prime out of the bag, and 5C2 ways to pick two non-primes, thus the 4 * 5C2 result samir had above. The same logic can be applied to the rest of the problem.

Just though that might help viewers a bit.

[arocks]

Nice explanations....btw....what's the source of this qu. Is that a previous GMAT qu...can it be solved faster...?

[samirpandeyit62]

Thanks ldoolitt, for explicitly mentioning this I forgot this (was in a little hurry).

by the way I forgot to mention one more thing

well the problem requires us to select 4 primes nos from 9, the approach that I've used above is in accordance to the sequence of events, so its a bit lenghty

However the best(fastest) approach would be to look at this problem in this

i.e after all these events eventually we will have 4 prime nos marbles in the cup, so this can be seen as selecting 4 prime marbles out of 9

i.e 4 marbles can be selected out of 9 in 9C4 = 126 ways

& all 4 prime in 1 way

so reqd probabilty is 1/126

[arocks]

Awwwsome!! that cracks it much faster....

[ri2007]

Hello Gabriel

Any idea if a question such as this one appears on the actual GMAT? Samir has been very helpful in showing how to solve this, but it looks much more complex than the std 3 steps needed to solve difficult GMAT questions.

Would be really useful to know what difficulty level one should expect. All OG questions seem really very simple in comparison.

Thanks so much

[jangojess]

u can expect Q like these as the difficulty level increases and provided u answer the previous Qs correctly...GMAT always try to test with TRICKY Qs and not DIFFICULT Qs....so always try to think a li'll bit out of the box...don't get urself bogged into the details...try to get the esence of the Q..."what is the end result???" "what is the basic thing tested??" it really helps in wordy PS and DS Qs....try to slice and dice a mosnter Q to simple equations...then anyone can solve the Q

[samirpandeyit62]

I completely agree with jangojess.

[RudeyBoyZ]

Dear Samir,

I have tried to use your logic, but in the second attempt once the 3 balls are collected, should'nt the probability to select 2 prime no. balls be 2/3 instead of 1/3??

Thanks in advance.

Warm Regards,

Rudraksh.

[RudeyBoyZ]

Dear Samir,

I have tried to use your logic, but in the second attempt once the 3 balls are collected, should'nt the probability to select 2 prime no. balls be 2/3 instead of 1/3??

Thanks in advance.

Warm Regards,

Rudraksh.