We can’t just write down any prime number; we need to make sure that when you subtract one prime number from the others that you get a prime number. Since every prime number except for ‘2’ is odd, when you subtract a prime number by a prime number you will end up with an even number. Since ‘2’ is the only even number, which two primes, less than 20, result in two when you subtract one from the other?

19 and 17

13 and 11

7 and 5

5 and 3

The other prime numbers will result when we subtract 2 from a prime number. Note, how this will be the same as the greater of the prime numbers in each pair above:

19 and 2

13 and 2

7 and 2

5 and 2

That gives us a total of 8 cases. For each case, however, there are two cases, since the question is asking for absolute difference. In other words, 11 and 13 = -2, the absolute difference is 2. This gives us a total of 16 cases.

The new step is to find the total number of possible outcomes:

Magoosh blog comment policy: To create the best experience for our readers, we will only approve comments that are relevant to the article, general enough to be helpful to other students, concise, and well-written! 😄 Due to the high volume of comments across all of our blogs, we cannot promise that all comments will receive responses from our instructors.

We highly encourage students to help each other out and respond to other students' comments if you can!

If you are a Premium Magoosh student and would like more personalized service from our instructors, you can use the Help tab on the Magoosh dashboard. Thanks!

why are we counting the additional 8 cases?both cards are picked together right?13 11 or 11 13 how does it make a difference?

Well explained! thank you so much for these valuable explanation i i will keep them in my mind! Bookmarking now

Hi Chris,

I have a question regarding MIS admission, did not get any blog for the same so I am posting it here.

I have a score of 308(Q:155, V:153). Can you help me with the colleges where I can get with these scores?

Thanks.

This is a conditional probability question.

Event A – the two cards are prime

Event B – difference between the two is prime

Now,

Prime nos from 0-20 = 8 and total nos = 21

P(A) = 8C2/21C2 = 2/15

We have to calculate P(B and A)

P(B and A) = P(A).P(BIA),

where P(BIA) is conditional probability of occurrence of B given A has already taken place.

There are 8 cases that satisfy B. Total no of cases are 28(Sum of total no of pairs of 8 prime nos), Thus

P(BIA) = 8/28

which gives P(BIA) = 2/15 * 8/28

= 4/105

@Utkarsh

Really helpful your explanation. And also MUCH faster than just counting the Integers..-.-