Final answer:
In this experiment, a bag with 5 red and 2 blue marbles is drawn from twice and replaced 100 times. The probability of drawing a blue marble on the first and second draw is 4/49. The expected number of times this will happen out of 100 experiments is 8.16.
Step-by-step explanation:
In this experiment, a bag contains 5 red marbles and 2 blue marbles.
Each marble is drawn twice and replaced 100 times.
The probability of drawing a blue marble on the first draw is 2/7, since there are 2 blue marbles out of 7 total marbles. After replacing the marble, the probability of drawing a blue marble again is still 2/7.
This is because the original proportions of marbles remain the same after each draw.
To calculate the probability of drawing a blue marble twice in a row, we multiply the probabilities together.
So the probability of drawing a blue marble on both the first and second draw is (2/7) * (2/7) = 4/49.
Finally, to calculate the expected number of times a blue marble will be drawn twice in a row out of 100 experiments, we multiply the probability by the number of experiments:
(4/49) * 100 = 8.16.