AP Statistics Simulations

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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

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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.