Statistics -Q32

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1) A probability experiment consists of rolling a 6-sided die. Find the probability of the event below.
rolling a number less than 4.

 
2) Use the frequency distribution to the right, which shows the number of voters (in millions) according to age, to find the probability that a voter chosen at random is in the given age range.
not between 18 to 20 years old between.

 
3) Determine whether the following statement is true or false. If it is false, rewrite it as a true statement.
If two events are independent,
 
P(A|B)equals=P(B). Choose the correct Answer below

A.
True
 
B.
False; if events A and B are independent, then
P(B|A)equals=P(A).
 
C.
False; if events A and B are independent, then P(A and
B)equals=P(A) times •P(B).
 
D.
False; if events A and B are independent, then P(A and
B)equals=0.

 

4) The table below shows the number of male and female students enrolled in nursing at a particular university for a recent semester.

(a) Find the probability that a randomly selected student is male, given that the student is a nursing major.

(b) Find the probability that a randomly selected student is a nursing major, given that the student is male.
Nursing Majors Non-nursing majors
Total

Males 9494 11241124 12181218
Females 713713 16351635 23482348
Total 807807 27592759 35663566

(a) Find the probability that a randomly selected student is male, given that the student is a nursing major.
 

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5) The table below shows the results of a survey in which 141 men and 146

women workers ages 25 to 64 were asked if they have at least one month’s income set aside for

emergencies. Complete parts (a) through (d).
Men Women Total

 

Less than one month’s income 65 84 149

One month’s income or more
76 62 138

Total 141 146 287

 

6) Determine whether the events E and F are independent or dependent. Justify your answer.
 
(a)
E: A person
living at least 70 yearsliving at least 70 years. 
F: The same person
regularly handling venomous snakes regularly handling venomous snakes.
 
A.
E and F are dependent because regularly handling venomous snakesregularly handling venomous snakes
can affect the probability of a person living at least 70 yearsliving at least 70 years.
 
B.
E and F are independent because regularly handling venomous snakes regularly handling venomous snakes
has no effect on the probability of a person living at least 70 yearsliving at least 70 years.
 
C.
E and F are dependent because living at least 70 yearsliving at least 70 years has no effect on the probability of a person regularly handling venomous snakes regularly handling venomous snakes.
 
D.
E and F are independent because living at least 70 yearsliving at least 70 years has no effect on the probability of a person regularly handling venomous snakesregularly handling venomous snakes.
 

7) In the general population, one woman in ten will develop breast cancer. Research has shown that 1 woman in 650 carries a mutation of the BRCA gene. Seven out of 10 women with this mutation develop breast cancer.
 
(a) Find the probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene.
 
The probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene is?

 

8) In a sample of 1200U.S. adults, 188 dine out at a restaurant more than once per week. Two U.S. adults are selected at random from the population of all U.S. adults without replacement. Assuming the sample is representative of all U.S. adults, complete parts (a) through(d).
 
(a) Find the probability that both adults dine out more than once per week.

The probability that both adults dine out more than once per week is?

 

According to a survey, 59% of the residents of a city oppose a downtown casino. Of these    
59% about 66 out of 10 strongly oppose the casino. Complete parts (a) through (c).
 
(a) Find the probability that a randomly selected resident opposes the casino and strongly opposes the casino.

(b) Find the probability that a randomly selected resident who opposes the casino does not strongly oppose the casino.

(c) Would it be unusual for a randomly selected resident to oppose the casino and strongly oppose the casino? Explain
 
The probability that a randomly selected resident opposes the casino and strongly opposes the casino is?

 

9) A standard deck of cards contains 52 cards. One card is selected from the deck.
 
(a)
Compute the probability of randomly selecting a diamondor heart.
(b)
Compute the probability of randomly selecting
Adiamondor heart or spade.
(c)
Compute the probability of randomly selecting a Sixor heart.
a. P(diamond or heart) equals=
(Round to three decimal places as needed.)

 

10) The percent distribution of live multiple-delivery births (three or more babies) in a particular year for women 15 to 54 years old is shown in the pie chart. Find each probability. A pie chart labeled “Number of Multiple Births” is divided into seven sectors with labels and approximate sizes as a percentage of a circle as follows: 15-19, 1.2 percent; 20-24, 6.3 percent; 25-29, 21.7 percent; 30-34, 37.1 percent; 35-39, 24.7 percent; 40-44, 5.4 percent; 45-54, 3.6 percent.
 
Number of Multiple Births
15-19 1.2%20-24 6.3%25-29 21.7%30-34 37.1%35-39 24.7%40-44 5.4%45-54 3.6%

a. Randomly selecting a mother 30-39 years old
P (30 to 39)almost equals≈
(Round to the nearest thousandth as needed.)

 
11) Evaluate the given expression and express the result using the usual format for writing numbers (instead of scientific notation).
 

43^(p)2=
 

12) Perform the indicated calculation.
Start Fraction (7^(c)4)/(11^(c)4)
 

13) Outside a home, there is a 4-key keypad with letters A,B,Cthat can be used to open the garage if the correct four-letter code is entered.

Each key may be used only once. How many codes are possible?
 

14) A horse race has 12 entries and one person owns 2 of those horses. Assuming that there are no ties, what is the probability that those two
horses finish first and second(regardless of order)?

 
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