A bag contains 8 white marbles and 2 black marbles. You pick out a marble, record its color, and put the marble back in the bag. If you repeat this process 45 times, how many times would you expect to remove a white marble from the bag?
36
8/10 * 45 = ?
To find the expected number of white marbles you would remove from the bag, we can use the concept of probability.
The probability of drawing a white marble from the bag is equal to the number of white marbles divided by the total number of marbles in the bag. In this case, there are 8 white marbles and 2 black marbles, so the probability of drawing a white marble is 8/(8+2) = 8/10 = 0.8.
Since you repeat the process 45 times and the probability of drawing a white marble remains the same for each draw, you can multiply the probability by the number of draws to get the expected number of white marbles:
Expected number of white marbles = probability of drawing a white marble x number of draws
Expected number of white marbles = 0.8 x 45 = 36.
So, you would expect to remove a white marble from the bag approximately 36 times.
To solve this problem, we need to find the probability of picking a white marble from the bag and then multiply it by the number of times the process is repeated.
In this case, the bag contains 8 white marbles and 2 black marbles, making a total of 10 marbles. The probability of picking a white marble is calculated by dividing the number of white marbles by the total number of marbles:
Probability of picking a white marble = Number of white marbles / Total number of marbles
= 8 / 10
= 0.8
So, there is an 80% chance of picking a white marble from the bag.
To find the expected number of times a white marble would be picked in 45 trials, we multiply the probability of picking a white marble by the number of trials:
Expected number of times = Probability of picking white marble * Number of trials
= 0.8 * 45
= 36
Therefore, you would expect to remove a white marble from the bag approximately 36 times in 45 trials.