GMAT Probability Practice Questions

To grow weekend ticket revenue, a farm runs a small wagon and a large wagon on the same 12-kilometer orchard loop. The small wagon averages 12 kilometers per hour, which is 3/2 times the large wagon's average speed. Each wagon runs for the full 6-hour selling day at a constant average speed, only completed loops are sold, loading time is ignored, and rider counts and completed loop counts are whole numbers. The small wagon carries 12 riders per loop and the large wagon carries 18 riders per loop. The fee for a loop is $60 if it has at most 15 riders; if it has more than 15 riders, the fee is $60 plus $4 for each rider above 15. One ticket is printed for each completed loop, all dollar amounts are per completed loop, all tickets are equally likely to be chosen, and two different tickets are drawn at random without replacement, so the first draw changes the ticket pool for the second draw. A pair is counted as meeting the growth target if the two fees total at least $132, with $132 included. What is the probability that the drawn pair meets the target?

A farmer has two fields: Field A produces 30 bushels of wheat with a 40% chance of being harvested successfully, and Field B produces 20 bushels with a 30% chance of being harvested successfully. What is the overall probability that a randomly chosen bushel from the total harvest is successfully harvested?

The manager of a pedestrian plaza is planning next season's event schedule. She surveyed the 72 people who visited the plaza during one lunch hour and asked each person which of that week's two scheduled plaza events he or she had attended: the Tuesday market, the Thursday concert, both, or neither. Each visitor fit exactly one of those four groups, and all counts are whole numbers of people. In all, 50 of the surveyed visitors had attended the market and 36 had attended the concert. The number of visitors who had attended both events was twice the number who had attended the concert but not the market. If one of the 72 surveyed visitors is selected at random, with every visitor equally likely to be chosen, what is the probability that the selected visitor had attended exactly one of the two events?

A manufacturing process produces widgets in batches of 100. In the first quality check, 1/5 of the widgets are rejected. In the second quality check, 1/4 of the remaining widgets are rejected. What is the probability that a randomly selected widget from the batch passes both quality checks?

A freight shipping company has three independent quality metrics for its shipments: 90% of shipments arrive safely, 75% are delivered on time, and 50% have correct documentation. What is the probability that a randomly selected shipment meets all three quality metrics?

A crew maintains nine distinct green spaces. The annual maintenance cost is $2,000 for each of three spaces, $3,000 for each of four spaces, and $5,000 for each of two spaces. Four distinct spaces are selected uniformly at random, without replacement. Given that the selection includes at least one space costing $5,000 to maintain, what is the probability that the total maintenance cost of the four selected spaces is at least $14,000?

A parking garage's ceiling clearance will decrease by 15 cm when the floor is repaved next month. The sum of the current clearance, in cm, and the clearance after the repaving, in cm, is 435. A vehicle can use the garage only if its height is less than or equal to the clearance.

The garage currently contains 10 vehicles, and all 10 fit under the current clearance. Every sedan is 150 cm tall, every van is 195 cm tall, and every truck is 215 cm tall. The number of sedans is a prime number, the number of vans is a prime number, the sum of these two numbers is odd, and there are 3 more sedans than vans. The remaining vehicles are trucks.

After the repaving, two different vehicles will be selected at random from the vehicles that will still be able to use the garage, with each vehicle in that group equally likely to be selected. What is the probability that at least one of the two selected vehicles is a van?

A workshop fires enamel tiles on a conveyor belt that carries each tile through a 60-centimeter hot zone at a steady belt speed. On Monday the belt moved at 5 centimeters per minute. On Tuesday the belt moved at 4/5 of the Monday speed. While in the hot zone, each tile shrinks 0.5% of its original length per minute. A tile that shrinks 7% or more of its original length is graded over-shrunk; every other tile is graded standard.

Every tile fired on those two days was placed in a bin, and the bin holds no other tiles. The tiles are stamped with consecutive numbers from 5 to 24, inclusive. Tiles numbered 5 through 9, inclusive, were fired on Monday, and tiles numbered 10 through 24, inclusive, were fired on Tuesday.

Two inspectors each draw one tile at random from the bin. The first inspector's tile is returned to the bin before the second inspector draws, so the two draws are independent and each draw is made from the full bin. Given that at least one of the two drawn tiles is over-shrunk, what is the probability that both drawn tiles are over-shrunk?

A film studio released 30 films last year. The ratio of dramas to comedies was 3:2. Among the dramas, the ratio of box office successes to failures was 2:1. Among the comedies, the ratio of successes to failures was 1:2. If a randomly selected film is a drama, what is the probability that it was a box office success?