QSCI381: Introduction to probability and statistics
Problem set #3
#1 Determine if each of the following is true or false. Explain why?
a. 20! - 17! = (20*19*18 - 1) *17! b. 12! = 4!*3!
c. 17!*0! = 16!*1! d. 15!/13! = 2!
e. 7! = 3!+4! f. 10P4 = 4!*(10C6)
#2 There are 10 jobs available for which there are 8 female and 12 male applicants. If half of the jobs are to be filled by females, in how many different ways can these 10 jobs be filled?
#3 If A & B are independent events with P(A) = 0.6 , P(B) = 0.5, find:
a. P(AÈ B); b. P(A’Ç B’);
c. P(B|A); d. P(A|B).
#4 Is there something wrong with the following statements? Explain your answer.
a. Probability that a mineral sample will contain copper is 0.30, gold 0.05, and both 0.0.
b. The events A & B, with P(A) = 0.6, and P(B) = 0.5, can not be mutually exclusive.
c. For two events A and B, P(A) = 0.7, P(B) = 0.9 and P(AÇ B) = 0.8
d. Two events A & B with probabilities P(A) = 0.6, and P(B) = 0.5 may be independent.
#5 A pool is stocked with 20 king and 10 pink salmon fish. Find the probability that a random catch of 5 fish will include:
a. all king salmons
b. all pink salmons
c. exactly three king and two pink salmons
d. at least one pink salmon.
#6 In a certain community, 8% of all adults over 50 have diabetes. A doctor in this community correctly diagnoses 95% of all persons who actually have diabetes and incorrectly diagnoses 2% of all persons without diabetes as having the disease. What is the probability that an adult over 50, diagnosed by this doctor as having diabetes actually has the disease?
What is your assessment of the reliability of the diagnostic test if the test result is negative (i.e., the test shows absence of the disease).