What’s the Chance? Dependent and Independent Trials
(from Activity-Based Statistics)
What is the probability that a tack lands point down?
Objective: To show how the probability of an event can be estimated by the relative
frequency of the event and how the accuracy of the estimate depends on the method of
estimation.
1. Collecting the data
a. Put a tack in a small jar or cup and toss the tack 10 times. Note the number of
times it lands point down, and find the relative frequency of a tack landing point
down. (# times lands point down / # tosses) This is your estimate of the
probability that a tack lands point down.
b. Collect the results from the rest of the class. You want to combine the results
of the tosses one student at a time and get a sequence of relative frequencies.
# of tosses
10 20 30 40 50…
# landing point down
Relative frequency
c. Instead of tossing one tack 10 times, put 10 tacks in the cup and toss the tacks
once.
d. Collect the results of these tosses from the class and complete a table similar
to that in part b.
2. Analyzing the data and drawing conclusions.
We can define the probability of a tack landing point down as the relative
frequency when a tack is tossed independently a large number of times. The
larger the number of tosses, the better out estimate of the probability.
a. Do the relative frequencies in the sequence in 1b converge toward a single
value? Can we use this value as our probability that a tack lands point down?
Verify that it satisfies the definition of probability. The probability that a tack
lands point down is approximately _____________.
b. Using the results in 1d, the probability that a tack lands point down is
Approximately______________.
Do the two sequences in part 1 converge to the same value and give us the
same probability? Are the experiments in 1a and 1c the same? Explain why you
think that the estimates of the probability should be different in the two cases.
c. Does our experiment of tossing 10 tacks simultaneously meet the conditions
required to estimate probability? Which probability estimates more accurately?