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# Molly is rolling a number cube with faces numbered 1 to 6

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Manager
Joined: 26 Sep 2013
Posts: 180
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Molly is rolling a number cube with faces numbered 1 to 6  [#permalink]

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24 Oct 2013, 09:07
11
00:00

Difficulty:

45% (medium)

Question Stats:

69% (02:01) correct 31% (01:57) wrong based on 300 sessions

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Molly is rolling a number cube with faces numbered 1 to 6 repeatedly. When she receives a 1, she will stop rolling the cube. What is the probability that Molly will roll the die less than 4 times before stopping?

A) 11/180

B) 125/216

C) 25/216

D) 91/216

E) 27/128
Math Expert
Joined: 02 Sep 2009
Posts: 65807
Re: Molly is rolling a number cube with faces numbered 1 to 6  [#permalink]

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24 Oct 2013, 09:15
4
5
AccipiterQ wrote:
Molly is rolling a number cube with faces numbered 1 to 6 repeatedly. When she receives a 1, she will stop rolling the cube. What is the probability that Molly will roll the die less than 4 times before stopping?

A) 11/180

B) 125/216

C) 25/216

D) 91/216

E) 27/128

will post OE after a few attempts

The probability that Molly will roll the die less than 4 times before stopping is the sum of the following:

The probability that Molly will roll the die once: P=1/6 (she gets 1 on the first roll);
The probability that Molly will roll the die twice: P=5/6*1/6 (not 1, 1);
The probability that Molly will roll the die thrice: P=5/6*5/6*1/6 (not 1, not 1, 1).

P = 1/6 + 5/6*1/6 + 5/6*5/6*1/6 = 91/216.

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Joined: 16 Oct 2010
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Re: Molly is rolling a number cube with faces numbered 1 to 6  [#permalink]

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28 Apr 2014, 20:55
2
ronr34 wrote:
Bunuel wrote:
AccipiterQ wrote:
Molly is rolling a number cube with faces numbered 1 to 6 repeatedly. When she receives a 1, she will stop rolling the cube. What is the probability that Molly will roll the die less than 4 times before stopping?

A) 11/180

B) 125/216

C) 25/216

D) 91/216

E) 27/128

will post OE after a few attempts

The probability that Molly will roll the die less than 4 times before stopping is the sum of the following:

The probability that Molly will roll the die once: P=1/6 (she gets 1 on the first roll);
The probability that Molly will roll the die twice: P=5/6*1/6 (not 1, 1);
The probability that Molly will roll the die thrice: P=5/6*5/6*1/6 (not 1, not 1, 1).

P = 1/6 + 5/6*1/6 + 5/6*5/6*1/6 = 91/216.

I tried looking at it this way:
1-(5/6)^4
what is wrong with this logic?

A small thing: It should actually be 1 - (5/6)^3

P(Less than 4 times) = 1 - P(4 times or more)

When will we roll the die 4 times or more? When we get something other than 1 in each of the first 3 rolls.

P(4 times or more) = (5/6)*(5/6)*(5/6)

P(Less than 4 times) = 1 - (5/6)*(5/6)*(5/6) = 91/216
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Karishma
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Joined: 07 Apr 2012
Posts: 310
Re: Molly is rolling a number cube with faces numbered 1 to 6  [#permalink]

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04 Nov 2013, 10:54
Bunuel wrote:
AccipiterQ wrote:
Molly is rolling a number cube with faces numbered 1 to 6 repeatedly. When she receives a 1, she will stop rolling the cube. What is the probability that Molly will roll the die less than 4 times before stopping?

A) 11/180

B) 125/216

C) 25/216

D) 91/216

E) 27/128

will post OE after a few attempts

The probability that Molly will roll the die less than 4 times before stopping is the sum of the following:

The probability that Molly will roll the die once: P=1/6 (she gets 1 on the first roll);
The probability that Molly will roll the die twice: P=5/6*1/6 (not 1, 1);
The probability that Molly will roll the die thrice: P=5/6*5/6*1/6 (not 1, not 1, 1).

P = 1/6 + 5/6*1/6 + 5/6*5/6*1/6 = 91/216.

I tried looking at it this way:
1-(5/6)^4
what is wrong with this logic?
Senior Manager
Joined: 05 Feb 2018
Posts: 440
Re: Molly is rolling a number cube with faces numbered 1 to 6  [#permalink]

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28 Jun 2019, 13:36
P(Roll 1 on 1st attempt OR Roll 1 on 2nd attempt OR Roll 1 on 3rd attempt)
Roll 1 on 1st = 1/6
Roll 1 on 2nd = 5/6*1/6 = 5/36
Roll 1 on 3rd = 5/6*5/6*1/6 = 25/216

1/6 + 5/36 + 25/216 =
(36 + 30 + 25) / 216 =
91 / 216
Re: Molly is rolling a number cube with faces numbered 1 to 6   [#permalink] 28 Jun 2019, 13:36