Common Sense Statistics Quiz, Q_01b

1. I have a bag with 25 koosh balls in it. Twenty are purple and five are green. I reach in and pick out a ball. What is the probability it is green?

P = 5/25 = 1/5 = .20

2. Using the same bag, I reach in 10 times, pick out a ball, and put it back in. How many purple ones do I expect to have picked out?

p(purple) = 4/5; 4/5 of 10 = 8

3. I have two bags that look alike. One, bag A, has 10 red and 10 yellow balls. The other, bag B, has 15 red and 5 yellow balls. I don't know which bag I am holding. I reach in 10 times, pick out a ball, and put it back in. I have picked out 8 red and 2 yellow balls. Which bag is it most likely that I am holding? Briefly, why?

You are most likely holding bag B, because the outcome of the experiment is more like what is expected from bag B.

In the experiment, p(red) = .8 and p(yellow) = .2

In bag A, p(red) = .5 and p(yellow) = .5

In bag B, p(red) = .75 and p(yellow) = .25

4. I have a bag with 25 koosh balls in it. Someone has told me that ten are orange and fifteen are brown. I reach in 10 times, pick out a ball, and put it back in. I have picked out only brown balls. Is it likely that the person's information is correct? Briefly, why?

No.

In the experiment, p(orange) = 0

In the hypothesized bag, p(orange) = 2/5

There is a very low probability of getting 0 orange out of 10 draws when nearly half are orange. The expected outcome of the experiment, 4 orange, is too different from the actual outcome, 0 orange, for us to accept the hypothesis.

5. I have a bag with koosh balls in it. I reach in 10 times, pick out a ball, and put it back in. Three of the balls are silver, one is white, and six are black. What is my best guess about the proportions of colors in the bag?

3:1:6, or .3:.1:.6

The best guess about the contents of the bag is what is observed in the sample.