GMAT Math : Calculating probability
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Example Questions
Example Question #11 : Data Interpretation
A die is rolled and then a coin is tossed. What is the probability that the die shows an even number AND the coin shows a tail?
We can calculate the two individual probabilities first.
Prob(die shows even) 
Prob(tail) 
Then, Prob(even AND tail) is 
Example Question #12 : Data Interpretation
A jar contains 8 blue marbles and 4 red marbles. What is the probability of picking a blue marble followed by a red marble if the first marble chosen is not put back in the jar?
There are 12 marbles total. The probability of picking a blue marble first is 
Example Question #12 : Probability
Refer to the above figure, which shows a target. Each of the squares is of equal size. If a dart is thrown at the target, what are the odds against hitting a red region?
You may assume that the dart hits the target, and you may disregard any skill factor.
There are fifteen ways to not hit a red region, and five ways to hit a red region. This makes the odds 15 to 5, or, in lowest terms, 3 to 1, against hitting a red region with a randomly thrown dart.
Example Question #12 : Probability
Sheryl is competing in an archery tournament. She gets to shoot three arrows at a target, and her best one counts.
Sheryl hits the bullseye 42% of the time. What is the probability (two decimal places) that she will hit the bullseye at least once in her three tries?
This is most easily solved by finding the probability that she will not hit the bullseye at all in her three tries. If she hits 42% of the time, she misses 58% of the time, and the probability she misses three times will be
The probability of hitting the bullseye at least once in three tries is the complement of this, or 
Example Question #14 : Probability
If you have a bag with 15 grey marbles, 15 yellow marbles and 20 green marbles, what is the probability of choosing a green marble followed by a yellow marble? Assume no replacement.
To calculate probability of multiple events, find the probability of each event and multiply them together. We begin with 50 total marbles in the bag.
For the first case, we are asked to pick a green marble. Because there are 20 green marbles and 50 total, our probability of this event is as follows:
For the second case, we need to pick a yellow marble. However, this time there are only 49 marbles left in the bag, because we didn't replace the green marble. Because we have 15 yellow marbles, the probability of this event is as follows:
To find our final answer, we need to multiply these two together.
Example Question #11 : Probability
If you flip a quarter three times, what is the probability of it landing on heads all three times?
Every time you flip a coin, there is a 1 in 2 chance of it landing on heads. So, if we want to know the probability of a coin landing on heads a certain number of times times in a row, we multiply the probability of that occurrence for however many times the coin is flipped. For three flips, this gives us:
So there is a 1 in 8 chance that a coin will land on heads three times in a row.
Example Question #13 : Probability
A drawer has 4 green socks, 6 blue socks, 12 white socks, 8 black socks, and 2 pink socks. If you reach in and pull out a sock at random, what is the probability the sock will be blue?
If you reach in and pull out a sock at random, the probability of it being blue is equal to the number of blue socks divided by the total number of socks in the drawer. First we'll calculate the total number of socks in the drawer:
Now we divide the number of blue socks by the total number of socks to find the probability of picking a blue sock:
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