Stat 200 – Statistics Problems – 5
9. A jar contains 10 blue marbles, 5 red marbles, 4 green marbles, and 1 yellow marble. Two marbles are chosen (without replacement).
(a) What is the probability that one will be green and the other red?
(b) What is the probability that one will be blue and the other yellow?
27. A refrigerator contains 6 apples, 5 oranges, 10 bananas, 3 pears, 7 peaches, 11 plums, and 2 mangos.
a. Imagine you stick your hand in this refrigerator and pull out a piece of fruit at 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 piece of fruit. You decide you do not want to eat that fruit so you put it back into the refrigerator and pull out another piece of fruit. What is the probability that the first piece of fruit you pull out is a banana and the second piece you pull out is an apple?
c. What is the probability that you stick your hand in the refrigerator one time and pull out a mango or an orange?
86. Roll two fair dice. Each die has six faces.
a. List the sample space.
b. Let A be the event that either a three or four is rolled first, followed by an even number. Find P(A).
c. Let B be 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 A and B mutually exclusive events? Explain your answer in one to three complete sentences, including numerical justification.
f. Are A and B independent
80. Florida State University has 14 statistics classes scheduled for its Summer 2013 term. One class has space available for 30 students, eight classes have space for 60 students, one class has space for 70 students, and four classes have space for 100 students.
a. What is the average class size assuming each class is filled to capacity?
Number of classes = 14
Number of spaces available = µ = (1*30 + 8*60 + 1*70 + 4*100) = 980
Average class size = 980/14 = 70
b. Space is available for 980 students. Suppose that each class is filled to capacity and select a statistics student at random. Let the random variable X equal the size of the student’s class. Define the PDF for X.
X
P(X)
30
30/980=0.031
60
(8*60)/980=0.490
70
70/980=0.071
100
(4*100)/7=0.404
c. Find the mean of X.
d. Find the standard deviation of X.
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