07 Jan 88.A school newspaper

5. A fair coin is flipped 9 times. What is the probability of getting exactly 6 heads?

7.You flip a coin three times.

(a) What is the probability of getting heads on onlyone of your flips?

(b) What is the probability of getting heads on at least one flip?

9. A jar contains 10 blue marbles, 5 red marbles, 4 green marbles, and 1 yellowmarble. Two marbles are chosen (without replacement).

(a) What is theprobability that one will be green and the other red?

(b) What is the probabilitythat one will be blue and the other yellow?

27. A refrigerator contains 6 apples, 5 oranges, 10 bananas, 3 pears, 7 peaches, 11plums, and 2 mangos.

a. Imagine you stick your hand in this refrigerator and pull out a piece of fruitat random. What is the probability that you will pull out a pear?

b. Imagine now that you put your hand in the refrigerator and pull out a pieceof fruit. You decide you do not want to eat that fruit so you put it back into therefrigerator and pull out another piece of fruit. What is the probability that thefirst piece of fruit you pull out is a banana and the second piece you pull out isan apple?

c. What is the probability that you stick your hand in the refrigerator one timeand pull out a mango or an orange?

5.

86.Roll two fair dice. Each die has six faces.

a. List the sample space.

b. Let Abe the event that either a three or four is rolled first, followed by an even number. Find P(A).

c. Let Bbe the event that the sum of the two rolls is at most seven. Find P(B).

d. In words, explain what “P(A|B)” represents. Find P(A|B).

e. Are Aand Bmutually exclusive events? Explain your answer in one to three complete sentences, includingnumerical justification.

f. Are Aand Bindependent events? Explain your answer in one to three complete sentences, including numericaljustification

6.

98.At a college, 72% of courses have final exams and 46% of courses require research papers. Suppose that 32% of courseshave a research paper and a final exam. Let Fbe the event that a course has a final exam. Let R be the event that a courserequires a research paper.

a. Find the probability that a course has a final exam or a research project.

b. Find the probability that a course has NEITHER of these two requirements.

112.Table 3.22identifies a group of children by one of four hair colors, and by type of hair.

HairType

Brown

Blond

Black

Red

Totals

Wavy

20

15

3

43

Straight

80

15

12

Totals

20

215

Table 3.22

a.Complete the table.

b.What is the probability that a randomly selected child will have wavy hair?

c.What is the probability that a randomly selected child will have either brown or blond hair?

d.What is the probability that a randomly selected child will have wavy brown hair?

e.What is the probability that a randomly selected child will have red hair, given that he or she has straight hair?

f.IfBis the event of a child having brown hair, find the probability of the complement ofB.

g.In words, what does the complement ofBrepresent?

8.

72.You buy a lottery ticket to a lottery that costs $10 per ticket. There are only 100 tickets available to be sold in thislottery. In this lottery there are one $500 prize, two $100 prizes, and four $25 prizes. Find your expected gain or loss.

9.

80.Florida State University has 14 statistics classes scheduled for its Summer 2013 term. One class has space available for30 students, eight classes have space for 60 students, one class has space for 70 students, and four classes have space for100 students.

a.What is the average class size assuming each class is filled to capacity?

b.Space is available for 980 students. Suppose that each class is filled to capacity and select a statistics student atrandom. Let the random variableXequal the size of the student’s class.Define the PDF forX.

c.Find the mean ofX.

d.Find the standard deviation ofX.

10.

88.A school newspaper reporter decides to randomly survey 12 students to see if they will attend Tet (Vietnamese NewYear) festivities this year. Based on past years, she knows that 18% of students attend Tet festivities. We are interested inthe number of students who will attend the festivities.

a. In words, define the random variable X.

b. List the values that Xmay take on.

c. Give the distribution of X. X ~ _____(_____,_____)

d. How many of the 12 students do we expect to attend the festivities?

e. Find the probability that at most four students will attend.

f. Find the probability that more than two students will attend.