Question

A bag has 6 blue cubes, 3 red cubes, and 3 green cubes. If you draw a cube and replace it in the bag 120 times, which of the following amounts would you expect to pull? Select all that apply. A) Pull a red cube 80 times B) Pull more red cubes than blue cubes C) Pull the same number of red and green cubes D) Pull two times as many blue cubes as red cubes E) Pull a blue cube 60 times

Answer 1

To find the expected number of times each event will occur, we need to calculate the probabilities of each event happening.

Step-by-step explanation:

To find the expected number of times each event will occur, we need to calculate the probabilities of each event happening. Here are the calculations for each event:

1. A) Pull a red cube 80 times: Since there are 3 red cubes out of 12 total cubes, the probability of pulling a red cube in one draw is 3/12. Therefore, the expected number of times pulling a red cube in 120 draws is (3/12) * 120 = 30 times.
2. B) Pull more red cubes than blue cubes: Since there are 6 blue cubes and 3 red cubes, it is not possible to pull more red cubes than blue cubes.
3. C) Pull the same number of red and green cubes: Since there are 3 red cubes and 3 green cubes, the probability of pulling a red or green cube in one draw is (3/12) + (3/12) = 6/12 = 1/2. Therefore, the expected number of times pulling a red or green cube in 120 draws is (1/2) * 120 = 60 times.
4. D) Pull two times as many blue cubes as red cubes: Since there are 6 blue cubes and 3 red cubes, the probability of pulling a blue cube in one draw is 6/12 = 1/2. Therefore, the expected number of times pulling a blue cube in 120 draws is (1/2) * 120 = 60 times. The expected number of times pulling a red cube in 120 draws is 30 times. Since 60 is two times 30, this statement is true.
5. E) Pull a blue cube 60 times: Since there are 6 blue cubes out of 12 total cubes, the probability of pulling a blue cube in one draw is 6/12 = 1/2. Therefore, the expected number of times pulling a blue cube in 120 draws is (1/2) * 120 = 60 times.