Table of Contents
- Introduction
- Probability of Independent Events
- Probability of Independent and Mutually Exclusive Events
- Probability of Independent and not Mutually Exclusive Events
Introduction
Probability is a measure of the chance that an event will occur. Probability in its most basic form can be found by taking the number of desired outcomes and dividing by the total number of possible outcomes.
Example
We have a jar with 4 red marbles and 6 blue marbles. What is the probability of drawing a red marble at random?
Of course if you’re targeting a 700+ score, the GMAT will likely not be asking such straightforward questions. To complicate problems, the GMAT will ask you to find the probability of two events occurring simultaneously or even sequentially.
Probability of Independent Events
If x and y are two independent events, find the probability that both event x and event y occur by multiplying the two probabilities together
Example
A dresser drawer contains one pair of socks in each of the following colors: blue, brown, red, white and black. Each pair is folded together in matching pairs. You reach into the sock drawer and choose a pair of socks without looking. The first pair you pull out is red -the wrong color. You replace this pair and choose another pair. What is the probability that you will choose the red pair of socks twice?
Probability of Independent and Mutually Exclusive Events
If x and y are independent events and mutually exclusive events, find the probability that either event x or event y will occur by adding the two probabilities together.
Example
From a bag containing 5 white balls, 2 black balls, and 11 red balls, 1 ball is drawn. What is the probability that the ball drawn is either black or red?
Probability of Independent and not Mutually Exclusive Events
If x and y are independent but not mutually exclusive events, add the probability that each event occurs individually and subtract the probability that both events occur together.
Example
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