## Mini-Quiz #1

Honor Code: You must do these problems on your own, and submit your answers no later than 11 PM on Sunday, September 30.

Name:

NetID (such as "abc123"):

Pick a personal (easy-to-remember) password (5-10 letters) for this course:

You awaken one lovely morning to find that the circus is in town!!! You go out to see the show.

In the opening act, 24 clowns emerge from a minivan. 11 have red noses, 9 have red hair, and 6 have neither.

How many have both a red nose and red hair? clowns

One of the clowns reaches into a bag containing 3 red and 7 black balls, and pulls out 4 of the balls at random.

What is the probability that 1 of the selected balls is red, and 3 are black? %

Hint: "Count" to get both the numerator and denominator. This problem is the same as asking: "If you draw a four-card hand from a 10-card deck containing 3 aces and 7 other cards, what is the probability that you'll end up with a exactly one of the aces?"

The clown throws three of the balls at the other clowns. Then, he repeatedly throws the last ball into the air, attempting to catch it on his head each time. On each toss, he has a 70% chance of catching the ball.

Using 50,000 simulation runs, estimate the probability that he catches the ball on at least 3 of his first 4 tries. %

What is the margin of error (at the 95%-confidence level) in your estimate? %

Hint: Use four "=IF"-based spreadsheet cells to simulate the outcomes of the four tosses: 1 if he catches the ball, and 0 otherwise. Then use the "=SUM" function to add up his successes, and an "=IF" formula which is 1 if he catches at least three of the balls, and 0 otherwise. Use KSim to "track" the average value of your final "=IF" formula.

When you are finished, click here: