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“Probability”- Ability to Deal with Fractions like a Pro

image4“The first step is to establish that something is possible; then probability will occur.”- Elon Musk

It is quite often heard from GMAT aspirants that Probability is one of the biggest challenges that deter their chances of doing well on the Quantitative section of the GMAT. Nevertheless, the concept of probability has same correlation with fractions (i.e. Part over Whole). So, in reality, the probability questions are fractions in disguise.

To understand this, let’s explore the definition first:

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You may see probability expressed on the GMAT in terms of a percent, a decimal, or a fraction.

What GMAC likes to test the most revolves around the rules mentioned below

  • Rule 1: Probability(Event Happens) + Probability(Event does not Happen) = 1
  • Rule 2: To find the probability of consecutive events, Probability of A and B = Probability of A × Probability of B
  • Rule 3: To find the probability that either event A OR event B occurs, add the probabilities of each event

Probability of A or B = Probability of A + Probability of B; when events are mutually exclusive
Probability of A or B = Probability of A + Probability of B – Probability (A and B); when events are not mutually exclusive.

Okay, so now after having an idea about the probability rules that can be seen on the GMAT, it’s time for some real business. Now we’ll discuss few questions which would give us an opportunity to embrace these ideas.

The Official Guide for GMAT Review 2017: Q-146, Page-171

Sixty percent of the members of a study group are women, and 45 percent of those women are lawyers. If one member of the study group is to be selected at random, what is the probability that the member selected is a woman lawyer?

a)0.10
b)0.15
c)0.27
d)0.33
e)0.45

Image-1An easy way to solve this question is by assuming a good number for total number of members. Let it be 100.

Thus, number of women = 60 and the number of woman lawyers = 0.45 × 60 = 27
Therefore, the probability of selecting a woman lawyer, P (Woman Lawyer) = 27/100 = 0.27

Hence, the answer is C.

Another way of asking the same question is “What fraction of members are women lawyer?” Interesting, hmmm…!

Let’s see what else can trouble us –

Roger wants to start his own family and they are planning to have three children. Assuming that the probability of having a girl or a boy child is same, what is the probability that he will have exactly two boys?

a)1/8
b)3/8
c)1/4
d)1/2
e)3/4

That seems tricky, right?  But you can nail it if you know the basics. A good point about this question is that you can apply two probability rules in this; i.e. Rule 2 & 3 as discussed earlier.

One thing to understand here is that since the probability of having a girl child or a boy child is same, both the events are equally likely to occur. Thus, the probability of having Boy = ½ and also the probability of having Girl = ½.

Since the individual probabilities are independent, they can be multiplied to figure out the combined probability.

P (Exactly 2 boys): P(BBG) or P(BGB) or P(GBB

= [½ × ½ × ½] + [½ × ½ × ½] + [½ × ½ × ½] )

=3 × [½ × ½ × ½]

Total Probability = 3 × (1/8) = 3/8

Hence, the answer is B.

What do you think about doing one more question? Yes…! Here it is:

image-3A fair coin is tossed three times. Find the probability of getting exactly two heads?

a)12.5%
b)25%
c)37.5%
d)50%
e)75%

Take two minutes to think about this. Okay, now what do you think is the answer? Isn’t it the same question as the last one? Yes, it is! So, the answer is C again.

The point is this that you may see same question in different forms and covered up in a different story in the GMAT and with a little practice of handful of rules you may get most of the probability questions correct. Isn’t it amazing?

Corollary:

    • Probability is your ability to critically think and understand what ‘needs to be done’
    • The rules are like pillars and once you understand them, you are a pro.
    • The GMAC® thinks that probability is such an elastic concept that it can incorporate other concepts into it easily. So, gear up as this topic is inevitable in the GMAT®

All the best! 🙂

 

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