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.

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.

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).

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.

Users browsing this forum: No registered users and 1 guest

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

GMAT(TM) and GMAT CAT (TM) are registered trademarks of the Graduate Management Admission Council(TM). The Graduate Management Admission Council(TM) does not endorse, nor is affiliated in any way with the owner or any content of this site.