# Objective : The student will be able to determine sample spaces

```Objective: The student will be able to determine sample spaces
From the information provided, create the sample space of possible
outcomes.
1) Flip a coin twice.
Solution: S = {HH, HT, TH, TT}
3) Both Fred and Ed have a bag of candy containing a lemon drop, a cherry
drop, and a lollipop. Each takes out a piece and eats it. What are the
possible pairs of candies eaten?
Solution: S = { lemon lemon, lemon cherry, lemon lollipop, cherry lemon,
cherry cherry , cherry lollipop, lollipop lemon , lollipop cherry , lollipop
lollipop}
4) Two white mice mate. The male has both a white and a black fur-color
gene. The female has only white fur-color genes. The fur color of the
offspring depends on the pairs of fur-color genes that they receive.
Assume that neither the white nor the black gene dominates. List the
possible outcomes.
Solution: S = {WW,BW}
Objective: The student will be able to ﬁnd the probability of an event,
using classical probability or empirical probability.
Find the indicated probability.
5) A sample space consists of 174 separate events that are equally likely.
What is the probability of each?
Solution: P = 1/174
6) On a multiple choice test, each question has 5 possible answers. If you
make a random guess on the first question, what is the probability that you
are correct?
Solution: P = 1/5
7) A die with 6 sides is rolled. What is the probability of rolling a number
less than 5?
Solution: P = 4/6 = 2/3
8) A bag contains 2 red marbles, 3 blue marbles, and 7 green marbles. If a
marble is randomly selected from the bag, what is the probability that it is
blue?
Solution: P = 3/12 = 1/4
9) Two 6-sided dice are rolled. What is the probability that the sum of the
two numbers on the dice will be 4?
Solution: P = 3/36 = 1/12
10) If a person is randomly selected, find the probability that his or her
birthday is in May. Ignore leap years.
Solution: P = 31/365 = 0.849
11) A class consists of 66 women and 98 men. If a student is randomly
selected, what is the probability that the student is a woman?
Solution: P = 66/164 = 0.402
12) The data set represents the income levels of the members of a country
club. Find the probability that a randomly selected member earns at least
101,000 105,000 87,000 107,000 92,000 101,000 97,000 77,000 111,000 121,000
82,000 99,000 109,000 92,000 105,000 103,000 97,000 113,000 72,000 103,000
Solution: P = 14/20 = 7/10 = 0.7
13) Refer to the table which summarizes the results of testing for a certain
disease.
If one of the results is randomly selected, what is the probability that it is a
false positive (test indicates the person has the disease when in fact they
don't)? What does this probability suggest about the accuracy of the test?
Solution: P = 26/273 = 0.095 , it must be very small value for the accuracy
of the test
14) Refer to the table which summarizes the results of testing for a certain
disease.
If one of the results is randomly selected, what is the probability that it is a
false negative (test indicates the person does not have the disease when in
fact they do)? What does this probability suggest about the accuracy of the
test?
Solution: P = 4/309 = 0.0129 , it must be very small value for the accuracy of
the test.
Estimate the probability of the event.
15) A polling firm, hired to estimate the likelihood of the passage of an upcoming referendum, obtained the set of survey responses to make its
estimate. The encoding system for the data is: 1 = FOR, 2 = AGAINST.
If the referendum were held today, estimate the probability that it would
pass.
1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1
Solution: P = 12/20 = 3/5 = 0.6
16) Of 1982 people who came into a blood bank to give blood, 340 people
had high blood pressure. Estimate the probability that the next person who
comes in to give blood will have high blood pressure.
Solution: P = 340/1982 = 0.171
Find the indicated complement.
17) If P(A) = 1/7
, find ̅̅̅̅
Solution: ̅̅̅̅= 1 – =
18) Find ̅̅̅̅, given that P(A) = 0.732.
Solution: ̅̅̅̅= 1 – 0.732 = 0.268
19) Based on meteorological records, the probability that it will snow in a
certain town on January 1st is 0.185. Find the probability that in a given
year it will not snow on January 1st in that town.
Solution: ̅̅̅̅ = 1 – 0.185 = 0.815
20) The probability that Luis will pass his statistics test is 0.90. Find the
probability that he will fail his statistics test.
Solution: ̅̅̅̅ = 1 – 0.90 = 0.10
21) If a person is randomly selected, find the probability that his or her
birthday is not in May. Ignore leap years.
Solution: ̅̅̅̅ 1 =
= 0.915
Find the indicated probability.
22) A spinner has equal regions numbered 1 through 21. What is the
probability that the spinner will stop on an even number or a multiple of
3?
Solution: P(A
= P(A) + P(B) – P(A
= + - = =
23) If you pick a card at random from a well shuffled deck, what is the
probability that you get a face card or a spade?
Solution: : P(A
= P(A) + P(B) – P(A
= + - = =
24-He should be able to find the probability of compound events , using
the addition rules when two events are mutually exclusive.
25- He should be able to find the probability of compound events , using
the addition rules when two events are not mutually exclusive.
26- He should be able to find the probability of compound events , using
when two events are not mutually exclusive.
(
)
27- He should be able to find the probability of compound events , using
the addition rules when two events are not mutually exclusive.
(
)
(
(
)
)
28- He should be able to find the probability of compound events , using
the addition rules when two events are mutually exclusive.
29- He should be able to find the probability of compound events
, using the addition rules when two events are mutually exclusive.
30- He should be able to find the probability of complementary events ,
using the rule.
31- He should be able to find the probability of two independent events ,
using the multiplication rules.
32- He should be able to find the probability of two independent events ,
using the multiplication rules.
33- He should be able to find the probability of two independent events ,
using the multiplication rules.
34- He should be able to find the probability of x successes in n trials of a
binomial experiment.
(
)
35- He should be able to find the probability of two independent events ,
using the multiplication rules.
36- He should be able to find the probability of two independent events ,
using the multiplication rules.
37- He should be able to find the probability of two independent events ,
using the multiplication rules.
38- He should be able to find the probability of two
independent events , using the multiplication rules.
39- He should be able to find the probability of x successes in n trials of a
binomial experiment.
( )( ) ( )
( )
40- He should be able to find the probability of x successes in n trials of a
binomial experiment.
41- He should be able to find the probability of x successes in n trials of a
binomial experiment.
```