MTH3003 SECOND SEMESTER SESSION 2013/14 TUTORIAL 2
1. A sample space S consists of five simple events with these probabilities: ) (a) (b)
Find the probabilities for simple events and Find the probabilities for these two events:
i. ii. (c)
List the simple events that are in both event
and event
2. A multiple-choice test has five questions, each with five choices for the answer. Only one of the choices is correct. You randomly guess the answer to each question. (a)
What is the probability that you answer the first question correctly?
(b)
What is the probability that you answer all five questions correctly?
(c)
What is the probability that you do not answer any of the questions correctly?
(d)
What is the probability that you answer at least one of the questions correctly?
3. A smoke detector system uses two devices, A and B. If smoke is present, the probability that it will be detected by device A is 0.95; by device B is 0.98 and by both devices is 0.94. (a) (b)
If smoke is present, find the probability that the smoke will be detected by device A or device B or both devices. Find the probability that the smoke will not be detected.
4. How many ways can a committee of six male and six female students be formed from twelve male and ten female students? 5. Two city council members are to be selected from a total of five to form a subcommittee to study the city’s traffic problems. (a) (b)
How many different subcommittees are possible? If all possible council members have an equal chance of being selected, what is the probability that members Smith and Jones are both selected?
1
6. The access code to a house’s security system consists of five digits. (a)
How many different codes are available if each digit can be repeated?
(b)
How many different codes are available if the first digit cannot be zero and the arrangement of five fives is excluded?
7. A television news director wishes to use three news stories on an evening show. One story will be the lead story, one will be the second story, and the last will be a closing story. If the director has a total of eight stories to choose from, how many possible ways can the program be set up? 8. The probability that Sam parks in a no-parking zone and gets a parking ticket is 0.06, and the probability that Sam cannot find a legal parking space and has to park in the noparking zone is 0.20. On Tuesday, Sam arrives at school and has to park in a no-parking zone. Find the probability that he will get a parking ticket. 9. Randomly selected 100 people were asked whether they were smoking or not. The following table gives a two-way classification of the responses obtained.
(a) (b) (c) (d) (e) (f) (g)
Smoking
Not smoking
Total
Male
19
41
60
Female
12
28
40
Total
31
69
100
What is the probability that randomly selected individual being a male who smokes? What is the probability of a randomly selected individual being a male? What is the probability of randomly selected individual smoking? What is the probability of randomly selected male smoking? What is the probability that a randomly selected smoker is male? Are the events “male” and “female” mutually exclusive? Are the event “male” and “not smoking” mutually exclusive? Why and why not? Are the events “male” and “smoking” independent? Why or why not?
10. There are three major manufacturing companies that make a product. Company A produce 50% of the total product, company B produce 30% of total product and company C produce 20% of total product. 5% of A’s product is defective, 7% of B’s product is defective, and 10% of C’s product is defective. (a) What is the randomly selected product is defective? (b) If a product is randomly selected, what is the probability that a defective product came from company B? 2
