# Probability -- Help?

posted by
**Cheri** on
.

Sampling one at a time with replacement from a bag with 8 blue, 7 red, and 5 green. What is the probability of getting at least two red in 3 draws? The book says the probability is 0.2818 but doesn't explain why. Any help????

Unfortunately, the probability of picking 3 red balls in a row is not obtained by just cubing the probability of the first draw.

After the first draw (7/30), the probability for the second draw changes to 6/29 and the third to 5/28. This is because the drawn balls are no longer in the pool of those to be drawn. However, if you are replacing the balls after they are drawn, this does not apply.

These changes need to be applied to the other problems.

I hope this helps a little more. Thanks for asking.

probability of drawing a red ball is 7/20. You have to add up the probability of 2 and 3 red balls out of 3 draws.

Probability of 3 red out of 3 is

(7/20)^3

Probability of 2 red out of 3 is

(7/20)^2*(13/20)*3

13/20 is the probability of drawing a ball of different color and the factor 3 is the number ways that lead to this outcome, i.e. you can draw the other ball the first time, the second time or the third time.

(7/20)^3 + (7/20)^2*(13/20)*3 = 0.28175

This problem is small enough to draw a probability tree. The probability of picking red on any draw is 7/20 = .35. Ergo, the probability of NOT picking red is 13/20 = .65.

So, the probability of picking red in all draws is .35*.35*.35

There are three ways to pick red 2 out of three times (d1,d2) (d1,d3), and (d2,d3). Each of these, separately, has a probability of .35*.35*.65

Take it from here.

hey i need help with theas 2 problems

prob.1[Ms. Madison sends 3 out of every 5 quilts she makes to a shop in Georgia.How many quilts are sent to the shop if she makes 20 quilts?

3/20 or 15%