# Ms. Stonebraker Show work. Simplify as you were directed during discussion time

 Дата канвертавання 27.04.2016 Памер 9.65 Kb.
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.

1. 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 .

 The probability that you draw a blue marble every time is or .

1. 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 non-green 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 - .

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 (1-p) = . 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 .

1. 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)

= + +
= + + .

 The probability that a purple marble is drawn at least 13 times is + + .

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