How to Practice Probability Questions on GRE

There are certain basic formulae that are required for solving questions on Probability. They are as follows:

Probability of an event happening =

The probability of an event will range from 0 to 1 that is 0 ≤ P (E) ≤ 1

P (event occurring) + P (event not occurring) = 1

Let us understand the use of these formulae by solving some questions.

1. A problem is given to Alan, Bob and Carl and their probability of solving it is1/2, 1/3 and 2/5 respectively. What is the probability that none of them solves the problem?

a) 1/5

b) 1/3

c) 1/2

d) 3/4

e) 11/12

Now the question asks for the probability of the problem not being solved by all three students.

P (Alan not solving AND Bob not solving AND Carl not solving) is what is asked.

It is given that P (Alan solving) =  1/2 , P (Bob solving) =  1/3 and P (Carl solving) = 2/5

P (Alan solving)

= 1/2

P (Alan not solving)  = 1- P (Alan solving)

= 1 –  1/2 =  1/2

P (Bob solving)          = 1/3

P (Bob not solving)   = 1-1/3

= 2/3

P (Carl solving)          =2/5

P (Carl not solving)   = 1-2/5  = 3/5

Therefore P (Alan not solving AND Bob not solving AND Carl not solving)

= 1/2 x 2/3 x 3/5

=  1/5

The point to be noted here is that when we use ‘AND’ we multiply.

The correct answer choice is A.

Now let us look at one more question.

2. Annie and Chris write the GRE on the same day. The probability of Annie getting a 170 in Math is 1/7 and the probability of Chris getting a 170 in Math is1/5. What is the probability that only one of them get 170 in Math?

1. 1/7
2. 2/7
3. 1/2
4. 3/4
5. 4/5

In this question we have to find the P (Exactly one of them getting 170).
So P (Exactly one of them getting 170) can be written as:

P (Annie getting a 170 in Math AND Chris not getting a 170 in Math) OR

P (Chris getting a 170 in Math AND Annie not getting a 170 in Math)

Here we see the use of both ‘AND’ and ‘OR’.
For ‘AND’ we multiply and for ‘OR’ we add.

Now the P (Annie getting a 170 in Math) = 1/7
P (Annie not getting a 170 in Math) =  6/7

P (Chris getting a 170 in Math) =  1/5
P (Chris not getting a 170 in Math) = 4/5

P (Annie getting a 170 in Math AND Chris not getting a 170 in Math) = 1/7 x 4/5

=  4/35

P (Chris getting a 170 in Math AND Annie not getting a 170 in Math) = 1/5 x 6/7

= 6/35

Putting both together we have:

P (Annie getting a 170 in Math AND Chris not getting a 170 in Math) OR
P (Chris getting a 170 in Math AND Annie not getting a 170 in Math)

= 4/35+6/35
= 10/35
= 2/7

The correct answer choice is B.

In our next blog on Probability, we will be seeing more questions on independent and dependent events.