Exercise 3.1

1.

Paula has 6 pairs of earrings in a box. She grabs two of the earrings in the box (sampling without replacement). Find the probability that she has a matched set of earrings.

 

Using the random number table, model this problem. (Hint: Use 0,1 for first pair; 2,3 for second pair; etc. Now the length of the trial is 2 (that's all she grabs and remember it's sampling without replacement). Next resample 10 trials of your model. For each trial record success (got a matched pair) or failure (did not get a matched pair). Obtain $\hat{p}$ your estimate of the desired probability. Calculate the error of estimation.

2.

When his alarm goes off, John hits the snooze button on it 80% of the time. If he fails to hit it, he gets up. The snooze alarm only works for 6 hits. Find the probability that John sleeps at least an extra 20 minutes. Using the random number table, model this problem. (Hint: Let 1-8 denote John hitting the button and 0,9 denote he doesn't. Note that the length of the trial is either 6 or when the first 0 or 9 occurs before 6.)

 

Next resample 10 trials of your model. For each trial record the extra sleep John got (for example, suppose the trial is 4, 6 ,9. Then John slept for an extra 20 minutes which is a success for the event we want). Obtain $\hat{p}$ your estimate of the desired probability. Calculate the error of estimation.

3.

20 passengers are on a bus that enters a foreign country. 12 of these passengers are women. At the gate to the foreign country, a guard gets on the bus and selects 6 people at random for an extensive visa check. Find the probability that (a) all 6 are males. Find the probability that (b) all 6 are females. Find the probability that (c) 4 are females.

 

Using the random number table, model this problem. Next resample 10 trials of your model. For each trial record the success or failure for each of (a), (b), and (c). Obtain $\hat{p}$ your estimate of the desired probability for each event. Calculate the error of estimation.

4.

Betty is playing 5 card draw poker. She holds 3 hearts and 2 clubs. In the draw, she decides to discard her 2 clubs and get two more cards. Find the probability that she will get a flush in hearts, i.e., her 2 cards in the draw are hearts.

 

Using the random number table, model this problem. Next resample 10 trials of your model. For each trial record the success or failure for the desired event. Obtain $\hat{p}$ your estimate of the desired probability. Calculate the error of estimation.

5.

Jack pays $10 to play a dice game in which 5 fair dice are rolled. If the dice result in:

(a)

All dice come up 6, Jack wins $500.

(b)

All dice are the same, Jack wins $100.

(c)

All dice are even, Jack wins $20.

(d)

Else Jack wins nothing.

Find the probability that Jack wins some money.

Using the random number table, model this problem. Next resample 10 trials of your model. For each trial record the success or failure for the desired event. Obtain $\hat{p}$ your estimate of the desired probability. Calculate the error of estimation.

2000-08-26