The bumper car ride at the state fair has 3 red cars, 4 green cars, and 2 blue cars. Joe is first in line for the ride and is assigned a car at random. Bill in next in line and is randomly assigned a car. What is the probability that both joe and bill will drive a red bumper car? Express your answer as a percent. If necessary, round your answer to the nearest tenth.
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Ryan has the numbers 1–30 listed on individual index cards. If Ryan randomly selects 1 card, what is the probability that it will be a multiple of 3 or a multiple of 11?
To calculate the probability that Joe and Bill will both drive a red bumper car, we need to know the total number of possible outcomes and the number of favorable outcomes.
First, let's determine the total number of possible outcomes. Since the cars are assigned randomly, Joe has 9 cars to choose from (3 red + 4 green + 2 blue), and Bill has 8 cars to choose from (assuming Joe takes one car). Therefore, the total number of possible outcomes is 9 * 8 = 72.
Next, let's calculate the number of favorable outcomes. Since there are 3 red cars, Joe has a 3/9 = 1/3 chance of getting a red car. After Joe takes a red car, there are 2 red cars left out of the remaining 8 cars for Bill, resulting in a 2/8 = 1/4 chance of Bill getting a red car. Therefore, the number of favorable outcomes is (1/3) * (1/4) = 1/12.
Finally, let's calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes: (1/12) / 72 = 1/864.
To express the answer as a percentage, we multiply the probability by 100 and round to the nearest tenth: (1/864) * 100 ≈ 0.1%.
Therefore, the probability that both Joe and Bill will drive a red bumper car is approximately 0.1%.