College Algebra 9th txtbk

554 CHAPTER 8 SEQUENCES, INDUCTION, AND PROBABILITY
(C) The expected frequencies are
E 1 : 500(.25) 125
E 2 : 500(.5) 250
E 3 : 500(.25) 125
The actual frequencies obtained from performing the experiment are reasonably close
to the expected frequencies. Increasing the number of trials of the experiment would
most likely produce even better approximations.
MATCHED PROBLEM 7
One die is rolled 500 times with the following frequencies of outcomes:
Outcome 1 2 3 4 5 6
Frequency 89 83 77 91 72 88
(A) Compute the approximate empirical probability for each outcome.
(B) Compute the theoretical probability for each outcome.
(C) Compute the expected frequency for each outcome.
Technology Connections
The data in Example 7 were not generated by tossing two
coins 500 times. Instead, the experiment was simulated by a
random number generator on a graphing calculator. The
command randint (0, 1, 500) produces a random sequence
of 500 terms; each term is 0 or 1 with equal liklihood. Thinking
of 1 as heads and 0 as tails, such a sequence represents
500 tosses of a single coin. Adding two such sequences
together produces a sequence of 500 terms in which each
term represents the number of heads in a toss of two coins
[see Fig. 3(a)]. We determine the frequency of each outcome
(0, 1, or 2 heads) in 500 tosses of two coins as follows: first,
we construct a histogram [Figs. 3(b) and 3(c)], then we use
the TRACE command to read off the frequencies [Figs. 3(d),
3(e), and 3(f)]. Compare with the data of Example 7.
If you perform the same simulation on your graphing calculator,
you are not likely to get exactly the same results.
But the approximate empirical probabilities you obtain will
be close to the theoretical probabilities.
(a) Generating the
random numbers
(b) Setting up the
histogram
(c) Selecting the
window variables
(d) 0 heads: 117 (e) 1 head: 262 (f) 2 heads: 121
Z Figure 3 Simulating 500 tosses of two coins.