In Class Exam 2 Review Math 166
1. A={a, b, c, d, e }
i) How many 10-long codes can be made from the letters in A?( no restrictions on the code )
ii) How many 3-long codes can be made from the letters in A if repeats are allowed?
iii) How many of those in ii) contain at least one “a”?
iii) How many 3-long codes from letters in A have no repeat letters?
iv) How many 3-element subsets does A have?
2. Fifteen jobs will be given to 80 people by drawing names.
i) How many ways can this be done if the jobs are all different and each name is replaced after it is drawn?
ii) How many ways can this be done if the jobs are all different and the names are not replaced?
iii) How many ways can this be done if the jobs consist of 1 foreman, 5 carpenters, and 9 painters and the names are not replaced?
3. How many 15-long codes can be made from the 26-letter alphabet that contain 2 a’s, 3 b’s, 4 c’s and 6 other different letters?
4. A coin is weighted so that P(H)=0.3. A box contains 3 red, 2 blue and 6 green balls.
An experiment consists of tossing the coin and selecting a ball and observing what is on top of the coin and the color of the ball. Write a probability distribution for this experiment.
5. Give some examples of mutually exclusive events.
If A and B are mutually exclusive events in a probability space with P(A)=0.5 and P(B)=0.4, find
i) P(A
B) ii) P(A
B)
6. Give an example of independent events.
If P(A)=0.7 and P(B)=0.8 find
i) P(AB) ii) P(AB)
7. Twenty people in a group each randomly choose a number between 1 and 100. What is the probability that:
a) at least two will choose the same number?
b) exactly two will choose the same number? (so there are no other repeats)
c) a specific two will choose the same number?
8. A graduate school has 80 applicants from school P and 120 from school Q. In general, 70% of school P applicants are accepted and 80% of these graduate. From school Q, 60% are accepted and 75% of these graduate.
a) Make a tree diagram for this information.
Find each probability:
a) An applicant from school P will graduate.
b) A graduate from this group is from school P.
c) An applicant is from school P and will graduate.