Simulate a Problem and Make an Organized List
COURSE 3 LESSON 11-6
On a multiple-choice test, each question has 4 possible
answers. You know the answers to all but the last two questions on
the test. Find the probability of guessing the answers to both
questions correctly.
Your goal is to find the probability that you will guess the answers to
two questions correctly. The probability of guessing correctly for each
question is 1 .
4
11-6
Simulate a Problem and Make an Organized List
COURSE 3 LESSON 11-6
(continued)
Method 1 Simulate the problem.
Simulate the problem by spinning a
spinner with four equal parts, A, B, C,
and D. Let A represent a correct guess
and B, C, and D represent an incorrect
guess. Two spins represent the last
two questions. Simulate 50 tests by
spinning the spinner 100 times.
Circle the test simulations where you
have two A’s.
11-6
AC
CB
AD
CD
CB
DD
DC
DA
CA
CB
100 Spins
BB CC DB
CA BC AC
DA CB BC
BC BC AA
AD CB DD
BB AB CD
AA DD DB
DB CC DC
CB DB DC
BD DA DD
CD
CC
CC
CA
AB
BC
CB
AD
CD
AC
COURSE 3 LESSON 11-6
Simulate a Problem and Make an Organized List
(continued)
The data shows that from 50 test simulations, AA occurs two times.
P(2 correct guesses) =
number of times AA occurs
total number of sets
2
= 50
Substitute.
1
Simplify.
= 25
1
The experimental probability is 25 , or 4%.
11-6
Simulate a Problem and Make an Organized List
COURSE 3 LESSON 11-6
(continued)
Method 2 Make an organized list.
Make an organized list to find all possible outcomes. The diagram shows
one correct guess and three incorrect guesses for each question.
The tree diagram shows that out of 16 possible outcomes, there is only
one outcome for two correct guesses.
11-6
Simulate a Problem and Make an Organized List
COURSE 3 LESSON 11-6
(continued)
number of times AA occurs
1
P(2 correct guesses) = total number of possible outcomes = 16
1
The theoretical probability is 16 , or 6.25%.
The experimental probability of 4% and the theoretical probability of 6.25%
are close in value. Check your results.
P(2 correct guesses) = P(correct) • P(correct)
1
1
= 4 • 4
Substitute.
1
= 16
Multiply.
This is the same probability you found by making an organized list.
11-6
Simulate a Problem and Make an Organized List
COURSE 3 LESSON 11-6
What is the probability that each of the last four digits of a
telephone number is an even number?
Sample answer: Assuming that all digits are equally likely,
the theoretical probability is
1
.
16
11-6