Read Me - Coin Toss Instructions (Word Format) (78.0K)

The Math Investigator is a data collection software program that may be used to collect data for the investigation. You may type answers onto the Word file or copy and paste in data from the Investigator.

Math Investigator 8.1

COIN TOSS SIMULATION on the Math Investigator simulates the toss of a coin up to 100 times and prints the sequence of heads and tails. The computer prints the empirical probability of obtaining a given number of heads or a number of consecutive heads.

1. If a coin is tossed twice, the probability of obtaining exactly 1 head is 50%.

a. Use Coin Toss Simulation and at least 30 repetitive trials to determine the empirical probabilities for each of the following events: tossing a coin 4 times and obtaining exactly 2 heads; tossing a coin 6 times and obtaining exactly 3 heads; tossing a coin 8 times and obtaining exactly 4 heads; etc.

b. Based on your observations from part a, write a conjecture about the probabilities of obtaining exactly 50% heads for larger and larger even numbers of tosses. Check your conjecture for some large even numbers and document whether or not your conjecture appears to be true.

2. The probability of obtaining at least k heads in tossing a coin n times can be investigated by Coin Toss Simulation.

a. Determine the empirical probabilities for the following events: obtaining at least 1 head in a toss of 2 coins; at least 2 heads in a toss of 4 coins; and at least 3 heads in a toss of 6 coins.

b. Use your data from part a to predict what will happen to the probabilities of obtaining at least 50% heads for larger and larger even numbers of tosses. Check your predictions for some large even numbers.

3. How many tosses of a single coin will have to be made before there is a 50% chance of obtaining at least 3 consecutive heads? Make a prediction and then use Coin Toss Simulation with at least 30 trials to gather data.

a. What is the empirical probability of tossing a coin 5 times and obtaining at least 3 consecutive heads?

b. What is the empirical probability of tossing a coin 6 times and obtaining at least 3 consecutive heads?

c. Experiment with different numbers of tosses to determine the number so that the probability of tossing at least 3 consecutive heads is 50%. Based on your data, what is this number of tosses?