Instructions

For this activity, you will need two coins. First, you will determine the theoretical probability of events. Then, you will flip the coins 100 times and determine the experimental probability of the events.

Flip two coins 100 times, and record the results of each coin toss in a table like the one below:

Result Frequency

Two heads

Two tails

One head, one tail

Answer the following questions based on the data you gathered. You must show your work to receive credit.

What is the theoretical probability that a coin toss results in two heads showing?

What is the experimental probability that a coin toss results in two heads showing?

What is the theoretical probability that a coin toss results in two tails showing?

What is the experimental probability that a coin toss results in two tails showing?

What is the theoretical probability that a coin toss results in one head and one tail showing?

What is the experimental probability that a coin toss results in one head and one tail showing?

Compare the theoretical probabilities to your experimental probabilities. Why might there be a difference?

I simulated the 100 coin flips for both coins, and I got the following results:

The theoretical probability that a coin toss results in two heads showing is 1/4. In fact, each coin shows heads with probability 1/2, and since the two coins are independent we multiply the probabilities.

The experimental probability that a coin toss results in two heads showing is 22/100=11/50, because I got two heads 22 times out of 100 tries.

The theoretical probability that a coin toss results in two tails showing is 1/4. In fact, each coin shows tails with probability 1/2, and since the two coins are independent we multiply the probabilities.

The experimental probability that a coin toss results in two tails showing is 30/100=3/10, because I got two tails 30 times out of 100 tries.

The theoretical probability that a coin toss results in one head and one tail showing is 2/4, because we count both heads-tails and tails-heads in this case, and each of them has probability 1/4 of occurring.

The experimental probability that a coin toss results in one head and one tail showing is 48/100=12/25, because I got one heads and one tails 48 times out of 100.

COMPARISONS:

For two heads, we expected 1/4 = 0.25 and got 11/50 = 0.22

For two tails, we expected 1/4 = 0.25 and got 3/10 = 0.3

For one heads and one tails, we expected 1/2 = 0.5 and got 12/25 = 0.48.

To explain this, consider for a moment the toss of a single coin. We expect heads and tails with probability 1/2 each, but this doesn't mean we will have, after many tries, exactly the same number of heads and tails. For example, if we toss the coin 100 times, all we can say is that 50 heads and 50 tails is the outcome that is more likely to occur, but it is very probable that we will get something like 49 heads and 51 tails, or vice versa, or maybe 48-52 or 47-53. Moreover, we can't even exclude, apriori, that we will get 100 heads or 100 tails. All we can say is how likely a certain event will be, considering its theoretical probability.

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