
It is currently Mon Apr 23, 2018 10:55 pm

View unanswered posts  View active topics

Page 1 of 1

[ 4 posts ] 

Author 
Message 
questioner

Post subject: GMAT Probability Posted: Sat Jul 10, 2010 1:37 pm 

Joined: Sun May 30, 2010 3:15 am Posts: 424

A password for a computer uses five digits from 0 to 9, inclusive. What is the probability that the digits of the password solely consist of prime numbers or zero? A. 1/32 B. 1/16 C. 1/8 D. 2/5 E. 1/2
(A) To calculate all the possibilities, there are 10 choices for each digit. The number of possibilities for five digits is 10 × 10 × 10 × 10 × 10 = 100,000 possible combinations.
Prime numbers constitute 2, 3, 5 and 7. In addition to zero, this is 5 total possibility for each digit. So the number of satisfactory variants is 5 × 5 × 5 × 5 × 5. So the probability is 1/2 × 1/2 × 1/2 × 1/2 × 1/2 = 1/32. The right answer is choice (A).  Please provide the formula and lesson overview which can enhance my understanding of the solution provided.


Top 


Gennadiy

Post subject: Re: GMAT Probability Posted: Sat Jul 10, 2010 2:16 pm 

Joined: Sun May 30, 2010 2:23 am Posts: 498

We can use general definition for probability: The number of satisfactory probabilistic events divided by the number of all possible probabilistic events.
The number of all the possible probabilistic events is 10 × 10 × 10 × 10 × 10
The number of satisfactory probabilistic events is 5 × 5 × 5 × 5 × 5
So the probability is (5 × 5 × 5 × 5 × 5) / (10 × 10 × 10 × 10 × 10) We simplify and get 1/2 × 1/2 × 1/2 × 1/2 × 1/2 = 1/32. In this case we used only general formula, described above.
Another way is to count probability for each digit to be prime or zero: 5/10 = 1/2. And since all the 5 digits must be prime or zero at once then these probabilities are multiplied: 1/2 × 1/2 × 1/2 × 1/2 × 1/2 = 1/32. In this case we used general formula, described above and rule for calculating probability of independent events happening at once.


Top 


ccheng

Post subject: Re: GMAT Probability Posted: Sat Oct 22, 2011 12:56 pm 

Joined: Mon Oct 10, 2011 1:25 pm Posts: 7

Why would you want to include 0 in part of the prime numbers. I though when it is an "or" problem you would add two separate events like (probability of getting the prime number) + (probability of getting zero).


Top 


Gennadiy

Post subject: Re: GMAT Probability Posted: Sun Oct 23, 2011 10:30 am 

Joined: Sun May 30, 2010 2:23 am Posts: 498

This wording implies that we consider 5 ordered digits: _ _ _ _ _ Each one of those can be either a prime number OR a zero. So the password can be: 0 2 2 7 3 0 0 0 0 0 7 2 0 5 3 5 5 7 7 2 etc.
If we had another wording, e.g. "the password consists of prime digits or it consists of zeroS", then it would imply that we consider 5 ordered digits: _ _ _ _ _ It could be 0 0 0 0 0 or 7 2 5 3 2, but it could NOT be 7 2 0 3 5.


Top 



Page 1 of 1

[ 4 posts ] 

Who is online 
Users browsing this forum: No registered users and 4 guests 

You cannot post new topics in this forum You cannot reply to topics in this forum You cannot edit your posts in this forum You cannot delete your posts in this forum You cannot post attachments in this forum

