Quiz 8 Solution Sheet
Math 1680
Ms. Stonebraker
Show work. Simplify as you were directed during discussion time.
Consider a bag that contains 3 purple marbles, 5 green marbles, 10 blue marbles, and 2 white marbles. Suppose you draw with replacement a marble out of the bag 15 separate times.

What is the probability that you draw a blue marble every time?
There is a total of 20 marbles and there are 10 blue marbles. Thus, the probability of drawing a blue marble is or . Thus having all 15 draws be a blue marble is or .


What is the probability that you draw a green marble at least once?
P(at least one green marble) = 1 – P(no green marbles) .
There are 20 total marbles and there are 5 green marbles, thus there are 15 nongreen marbles. Thus the probability of not drawing a green marble is or . Thus having all 15 draws not be a green marble is or .
P(at least one green marble) = 1 – P(no green marbles) = 1  .

P(at least one green marble) = 1  .


What is the probability that a purple marble is drawn exactly 13 times?
We can make use of the binomial formula for this problem. There are 15 draws thus n = 15. A success is going to be labeled drawing a purple marble. Thus the probability of drawing a purple marble or the probability of a success is . Thus p = . Hence (1p) = . When we consider when there are exactly 13 purple marbles drawn, k = 13. Thus the solution using binomial formula is as follows:
= = =
= = .

The probability that a purple marble is drawn exactly 13 times is .


What is the probability that a purple marble is drawn at least 13 times?
P(at least 13 purple) = P(exactly 13 purple) + P(exactly 14 purple) + P(exactly 15 purple)
= + +
= + + .
