AP Statistics Simulations

Please see the accompanying table.

I toss a penny and observe whether it lands heads up or tails up. Suppose the penny is fair, i.e., the probability of heads is 1/2 and the probability of tails is 1/2. This means that

• every occurrence of a head must be balanced by a tail in one of the next two or three tosses.

• if I flip the coin 10 times, it would be almost impossible to obtain 7 heads and 3 tails

• if I flip the coin many, many times the proportion of heads will be approximately 1/2, and this proportion will tend to get closer and closer to 1/2 as the number of tosses increases.

• regardless of the number of flips, half will be heads and half tails.

• all of the above.

You want to use simulation to estimate the probability of getting exactly one head and one tail in two tosses of a fair coin. You assign the digits 0, 1, 2, 3, 4 to heads and 5, 6, 7, 8, 9 to tails. Using the following random digits to execute as many simulations as possible, what is your estimate of the probability?

19226 95034 05756 07118

• 1/20

• 1/10

• 5/10

• 6/10

• 2/3

what is the probability that you draw either a brown or a green candy?

• 0.1.

• 0.3.

• 0.4.

• 0.6.

• 0.7.

• A

• B

• C

• D

• E

• A

• B

• C

• D

• E

Please see the accompanying table.

Please see the accompanying table.

Please see the accompanying table.

When two coins are tossed, the probability of getting two heads is 0.25. This means that

• of every 100 tosses, exactly 25 will have two heads.

• the odds against two heads are 4 to 1.

• in the long run, the average number of heads is 0.25.

• in the long run two heads will occur on 25% of all tosses.

• if you get two heads on each of the first five tosses of the coins, you are unlikely to get heads the fourth time.