GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 11 Nov 2019, 12:25 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Jay Z is rolling a number cube with faces numbered 1 to 6

Author Message
TAGS:

### Hide Tags

Manager  Joined: 17 Jul 2010
Posts: 109
Jay Z is rolling a number cube with faces numbered 1 to 6  [#permalink]

### Show Tags 00:00

Difficulty:

(N/A)

Question Stats: 100% (01:02) correct 0% (00:00) wrong based on 5 sessions

### HideShow timer Statistics

Jay Z is rolling a number cube with faces numbered 1 to 6 repeatedly. When he receives a 4, he will stop rolling the cube. What is the probability that Jay Z will roll the die less than 3 times before stopping?

Please explain in detail, I'm having problems setting the problem up. If there are multiple ways of setting the problem up, please list those possibilities, thanks!
Magoosh GMAT Instructor G
Joined: 28 Dec 2011
Posts: 4468
Re: P(A) + P(Not A) = 1  [#permalink]

### Show Tags

1
laythesmack23 wrote:
Jay Z is rolling a number cube with faces numbered 1 to 6 repeatedly. When he receives a 4, he will stop rolling the cube. What is the probability that Jay Z will roll the die less than 3 times before stopping?

Please explain in detail, I'm having problems setting the problem up. If there are multiple ways of setting the problem up, please list those possibilities, thanks!

Hello! I'm happy to help with this. This is a relatively challenging probability question --- this is typical, for example, of a question on probability theory that the AP Statistics exam would ask. This is getting toward the outer limit of anything the GMAT would ask about probability.

First, let's think about an individual trial ---- one roll of the die. We are going to call getting a 4 a "success." On one trial,
P(success) = 1/6
and
P(not success) = 5/6

Now, we have to figure out the probability of getting a successful trial in fewer than three trials.
(BTW --- grammar point important for GMAT SC -- it should be fewer than three trials, not less than three trials, because trials are countable. See:
http://magoosh.com/gmat/2012/gmat-gramm ... -vs-fewer/)

Let N = the number of the trial on which the first successful trial occurs.

The restriction "fewer than three trials" means we are looking at the cases N = 1 or N = 2 only.

Case #1: N = 1
In this scenario, we toss the cube once and it's successful. Probability = 1/6

Case #2: N = 2
This scenario involves two tosses, and has the requirements (a) the first toss is not a success, and (b) the second toss is a success. Because those two are joined by the word "and", that means multiply in probability.
P(1st toss = not success and 2nd toss = success) = (5/6)*(1/6) = 5/36

Calculating the total probability involves an "or" statement --- in probability, "or" means add.
P(N<3) = P(N= 1 or N = 2) = 1/6 + 5/36 = 11/36

Does all this make sense?

Mike _________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Manager  Joined: 17 Jul 2010
Posts: 109
Re: P(A) + P(Not A) = 1  [#permalink]

### Show Tags

mikemcgarry wrote:
laythesmack23 wrote:
Jay Z is rolling a number cube with faces numbered 1 to 6 repeatedly. When he receives a 4, he will stop rolling the cube. What is the probability that Jay Z will roll the die less than 3 times before stopping?

Please explain in detail, I'm having problems setting the problem up. If there are multiple ways of setting the problem up, please list those possibilities, thanks!

Hello! I'm happy to help with this. This is a relatively challenging probability question --- this is typical, for example, of a question on probability theory that the AP Statistics exam would ask. This is getting toward the outer limit of anything the GMAT would ask about probability.

First, let's think about an individual trial ---- one roll of the die. We are going to call getting a 4 a "success." On one trial,
P(success) = 1/6
and
P(not success) = 5/6

Now, we have to figure out the probability of getting a successful trial in fewer than three trials.
(BTW --- grammar point important for GMAT SC -- it should be fewer than three trials, not less than three trials, because trials are countable. See:
http://magoosh.com/gmat/2012/gmat-gramm ... -vs-fewer/)

Let N = the number of the trial on which the first successful trial occurs.

The restriction "fewer than three trials" means we are looking at the cases N = 1 or N = 2 only.

Case #1: N = 1
In this scenario, we toss the cube once and it's successful. Probability = 1/6

Case #2: N = 2
This scenario involves two tosses, and has the requirements (a) the first toss is not a success, and (b) the second toss is a success. Because those two are joined by the word "and", that means multiply in probability.
P(1st toss = not success and 2nd toss = success) = (5/6)*(1/6) = 5/36

Calculating the total probability involves an "or" statement --- in probability, "or" means add.
P(N<3) = P(N= 1 or N = 2) = 1/6 + 5/36 = 11/36

Does all this make sense?

Mike Yes it makes sense, in fact, I thought the same thing, I've been doing a lot of GMAT problems, and when I needed to review for my final push, the MGMAT Book uses a similar example, and I was not sure if it was relevant for what is asked on the GMAT.
Director  Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 840
Location: India
GMAT 1: 410 Q35 V11 GMAT 2: 530 Q44 V20 GMAT 3: 630 Q45 V31 GPA: 3.84
WE: Engineering (Transportation)
Re: Jay Z is rolling a number cube with faces numbered 1 to 6  [#permalink]

### Show Tags

1
Its a kind of brain teaser.

We have to find the probability that he gets 4 in 1st attempt or in the 2nd attempt
Calculate individual probab, for 1st attempt it is 1/6
For 2nd attempt it is 5/6 and 1/6 equals to 5/36

Finally 1st attempt or 2nd attempt
= 1/6 +5/36
=11/36 Re: Jay Z is rolling a number cube with faces numbered 1 to 6   [#permalink] 12 Dec 2012, 14:40
Display posts from previous: Sort by

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