In box A, there are 10 red marbles, 10 green marbles and 10 yellow mar

Question

In box A, there are 10 red marbles, 10 green marbles and 10 yellow marbles. Jack takes turn in picking randomly a marble from that box. What is the probability that Jack picks 4 marbles that have the same color?

A. 2/87
B. 16/29
C. 2/261
D. 28/1131
E. 28/3393

A. 2/87
B. 16/29
C. 2/261
D. 28/1131
E. 28/3393

BrentGMATPrepNow · Answer

P(4 matching marbles) = P(1st is ANY color   AND   2nd marble matches 1st   AND   3rd marble matches 1st   AND   4th marble matches 1st)
= P(1st is ANY color)   x   P(2nd marble matches 1st)   x   P(3rd marble matches 1st)   x   P(4th marble matches 1st)
= 30/30   x   9/29   x   8/28   x   7/27
= 1   x   9/29   x   2/7   x   7/27
= (9)(2)(7)/(29)(7)(27)
= (9)(2)/(29)(27)
= (1)(2)/(29)(3)
= 2/87

Answer: A

PSKhore · Answer

Method 1:

(10/30)*(9/29)*(8/28)*(7/27)*3
...multiplying by 3 because there are 3 colors

Method 2:

*3
 ...multiplying by 3 because there are 3 colors

=2/87

ADhanjal · Answer

Bunuel 
How do I determine the correct approach for this probability problem? The question says, "Jack takes turn in picking randomly a marble from that box." I guess, which means he is taking out 1 marble each time without replacement until he has 4 marbles. I used Approach 2 and got it wrong; Approach 1 is correct. 
Approach 1: (10C4)/(30C4) 
Approach 2: (10C1*9C1*8C1*7C1)/(30C4)

Bunuel · Answer

Correct approaches are given  HERE  and  HERE . Please let me know if anything is unclear there.

ADhanjal · Answer

I’ve figured out where I went wrong in the previous problem, but I still struggle with deciding which approach to use when the wording is unclear. For example, the question said, “Jack takes turns picking randomly a marble from that box,” which suggests he picks one marble at a time without replacement, so the combination approach was correct. However, in some questions, it’s left ambiguous whether the person picks all the items at once or one by one. Are these situations truly ambiguous, or will there always be a hint in the wording that they are picking one by one? If it is ambiguous, is it safer to assume they pick all at once using combinations? I’d appreciate any tips on how to interpret these cases.

Bunuel · Answer

1. A proper GMAT question will be very precise and clear, so it will not leave room for multiple interpretations.

2. Mathematically, picking “one by one without replacement” or “all at once” is the same thing.

For example, suppose a box has 3 red and 2 blue marbles and you want the probability of getting 2 reds when picking twice without replacement :

All at once (combinations): C(3,2)/C(5,2) = 3/10 
 One after another without replacement: P(R then R) = 3/5 * 2/4 = 3/10

Same answer.

3. The difference is not “one by one vs all at once,” but “with replacement vs without replacement.” That is what changes the probability. And again, a proper GMAT question will clearly state if the drawing is with or without replacement.

Hope it helps.

ravi1522 · Answer

Hello ,
In box A, there are 10 red marbles, 10 green marbles and 10 yellow marbles. Jack takes turn in picking randomly a marble from that box. What is the probability that Jack picks 4 marbles that have the same color?
favorable cases probability will be 4 red marbles or 4 green marbles or 4 yellow marbles

10C4+10C4+10C4/30C4

when you solve you get 2/87
Hence option A is correct

In box A, there are 10 red marbles, 10 green marbles and 10 yellow mar

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In box A, there are 10 red marbles, 10 green marbles and 10 yellow mar

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