GMAT Math : Calculating probability

Example Questions

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Example Question #1 : Probability

Two dice are rolled. What is the probability that the sum of both dice is greater than 8?

Explanation:

There are 36 possible outcomes (). 10 out of the 36 outcomes are greater than 8: (6 and 3)(6 and 4)(6 and 5)(6 and 6)(5 and 4)(5 and 5)(5 and 6)(4 and 5)(4 and 6)(3 and 6).

Example Question #2 : Probability

Among a group of 300 people, 15% play soccer, 21% play baseball, and 9% play both soccer and baseball. If one person is randomly selected, what is the probability that the person selected will be one who plays baseball but NOT soccer?

Explanation:

Since there are 300 people,  people play baseball and  of those people play both baseball and soccer. Therefore, there are  people who play baseball but not soccer.

Probability:

Example Question #3 : Probability

If a die is rolled twice, what is the probability that it will land on either 2 or an odd number both times?

Explanation:

probability on one roll:

for both times=

Example Question #4 : Probability

What is the probability of sequentially drawing 3 aces from a deck or regular playing cards when the selected cards are not replaced?

Explanation:

The probability of drawing an ace first is  or .

Assuming an ace is the first card selected, the probability of selecting another ace is  or .

For the third card, the probability is  or .

To calculate the probability of all 3 events happening, you must multiply the probabilities:

Example Question #5 : Probability

How many even four-digit numbers larger than 4999 can be formed from the numbers 2, 4, 5, and 7 if each number can be used more than once?

Explanation:

Since the number must be larger than 4999, the thousand’s digit has to be 5 or 7. We are also told that the number must be even. Thus, the unit’s digit must be 2 or 4. The middle digits can by any of the numbers 2,4,5, or 7. Therefore, we have a total of  possibilities.

Example Question #191 : Word Problems

What is the probability of rolling an even number on a standard dice?

Explanation:

A standard dice has 6 faces numbered .

There are  even numbers, , divided by the total number of faces:

Example Question #7 : Probability

Shawn is competing in an archery tournament. He gets to shoots three arrows at a target, and his best two shots count.

He hits the bullseye with 40% of his shots. What is the probability that he will hit the bullseye at least twice out of the three times?

Explanation:

There are three scenarios favorable to this event.

1: He hits a bullseye with his first two shots; the third shot doesn't matter.

The probability of this happening is

2: He hits a bullseye with his first shot, misses with his second shot, and hits with his third shot.

The probability of this happening is

3: He misses with his first shot and hits a bullseye with his other two shots.

The probability of this happening is

Example Question #8 : Probability

A store uses the above target for a promotion. For each purchase, a customer gets to toss a dart at the target, and the outcome decides his prize. If he hits a pink region, he gets nothing; if he hits a red region, he gets a 10% discount on a future purchase; if he hits a green region, he gets a 20% discount; if he hits a blue region, he gets a 40% discount.

Assume a customer hits the target and no skill is involved. What are the odds against him getting a discount?

Explanation:

The customer gets a discount if he does not hit a pink region. There are ten out of twenty ways to hit a pink region and ten to not hit one - this makes the odds 10 to 10, or, in  lowest terms, 1 to 1 against a discount.

Example Question #9 : Probability

It costs $10 to buy a ticket to a charity raffle in which three prizes are given - the grand prize is$3,000, the second prize is $1,000, and the third prize is$500. Assuming that all of 1,000 tickets are sold, what is the expected value of one ticket to someone who purchases it?

Explanation:

If 1,000 tickets are sold at $10 apiece, then$10,000 will be raised. The prizes are $3,000,$1,000, and $500, so$4,500 will be given back, meaning that the 1,000 ticket purchasers will collectively lose \$5,500. This means that on the average, one ticket will be worth

This is the expected value of one ticket.

Example Question #1 : Probability

Daria has 5 plates: 2 are green, 1 is blue, 1 is red, and 1 is both green and blue. What is the probability that Daria randomly selects a plate that has blue OR green on it?