Groups in math class have 4 green marbles, 6 yellow marbles, and 10 black marbles. Each group pulls out a marble, records it, and then replaces it 50 times. The class complies its data. how many times can you expect to pull out a green marble with 1000 pulls?
To find out how many times you can expect to pull out a green marble with 1000 pulls, we need to calculate the probability of pulling out a green marble for each pull and then multiply it by the total number of pulls.
In a single pull, there are 20 marbles in total (4 green + 6 yellow + 10 black).
The probability of pulling out a green marble in one pull is 4/20, since there are 4 green marbles out of the 20 total marbles.
To find the probability of not pulling a green marble in a single pull, we can calculate it as 1 - (4/20), which is 16/20.
Now, we can calculate the probability of not pulling a green marble in all 1000 pulls. Since each pull is independent, we can multiply the probabilities of not pulling a green marble in each pull:
(16/20) * (16/20) * (16/20) * ... (1000 times)
To simplify this calculation, we can raise the probability of not pulling a green marble (16/20) to the power of the total number of pulls (1000):
(16/20) ^ 1000
Now, calculate the probability of pulling a green marble in each pull:
1 - (16/20) ^ 1000
Finally, multiply this probability by the total number of pulls (1000) to find out how many times you can expect to pull out a green marble with 1000 pulls:
(1 - (16/20) ^ 1000) * 1000
By solving this equation, you can find the expected number of times you can pull out a green marble with 1000 pulls.