Without looking, Tammy takes a marble out of a bag that contains 10 red marbles, 15 green marbles, and 25 blue marbles. She records its color and returns the marble to the bag. If Tammy repeats the proess 90 times, how many times can she expect to pull a red marble? Please explain, I don't get this. Thank you and God bless you.
Since there are 10 reds out of 50 marbles,
the prob(red) = 10/50 = 1/5
Since the marble is returned, each turn is independent on the results of any previous or future draw
So in 90 draws we expect (1/5)(90) or 18 reds
10/50 of the total draws
Thank you very much, I kindly appreciate you both. God bless you both.
To find out how many times Tammy can expect to pull a red marble, we need to understand the concept of probability. Probability is the measure of the likelihood of an event occurring.
In this case, the probability of pulling a red marble is the number of red marbles divided by the total number of marbles.
So, out of the 10 red marbles, the probability of pulling a red marble on the first try is 10/50 (since there are a total of 50 marbles in the bag).
Since Tammy records the color and returns the marble to the bag, the probability remains the same for each subsequent try. Therefore, each time Tammy pulls a marble, the probability of pulling a red marble is still 10/50.
Since Tammy repeats the process 90 times, the expected number of times she can pull a red marble can be calculated by multiplying the probability of pulling a red marble (10/50) by the number of trials (90):
Expected number of times = Probability of pulling a red marble * Number of trials
= (10/50) * 90
Simplifying this expression, we get:
Expected number of times = (10/50) * 90
= (1/5) * 90
= 18
Therefore, Tammy can expect to pull a red marble around 18 times out of the 90 times that she repeats the process.