Q1: Among 10 laptop computers, five are good and five have defects. Unaware of this, a

customer buys 6 laptops.

a) What is the probability of exactly 2 defective laptops among them?

b) Given that at least 2 purchased laptops are defective, what is the probability that exactly 2

are defective?

Q2: Suppose that after 10 years of service, 40% of computers have problems with motherboards,

30% have problems with hard discs and 15% have problems with both motherboard and hard

disc. What is the probability that 10 year old computer has fully functioning motherboard and

hard disc?

Q3: A new computer virus can enter the system through email or through the internet. There is a

30 % chance of receiving this virus through email. There is a 40 % chance of receiving it through

the internet. Also, the virus enters the system simultaneously through email and the internet with

probability 0.15. What is the probability the virus does not enter the system at all?

Q4: There are 10 teaching assistants available for grading papers in a calculus course at a large

university. The first exam consist of four questions, and the professor wishes to select a different

assistant to grade each question (only one assistant per question). In how many ways can the

assistance be chosen for grading?

Q5: There are 1% probability for a hard drive to crash. Therefore, it has two backups and each

having 2% probability to crash, and all three components are independent of each other. The

stored information is lost only in an unfortunate situation when all three devices crash. What is

the probability that information is saved?

Q6: Suppose that a shuttle's launch depends on three key devices that operate independently of

each other and malfunction with probabilities 0.01, 0.02 and 0.02, respectively. If any of the key

devices malfunctions, the launch will be postponed. Compute the probability for the shuttle to be

launched on time, according to its schedule?

Q7: 90% of flights depart on time. 80% of flights arrive on time. 75% of flights depart on time

and arrive on time.

You are meeting a flight that departed on time. What is the probability that it will arrive

on time?

You have met a flight, and it arrived on time. What is the probability that it departed on

time?

Are the events, departing on time and arriving on time, independent?

Q8: A computer program is tested by 3 independent tests. When there is an error, these tests will

discover it with probabilities 0.2, 0.3 and 0.5, respectively. Suppose that the program contains an

error. What is the probability that it will be found by at least one test.

Q9: A system may become infected by some spyware through the internet or email. 70% of the

time the spyware arrives via the internet, 30 % of the time via email. If it enters via the internet,

the system detects it immediately with probability 0.6. If via email, it is detected with probability

0.8. What percentage of times is this spyware detected?

Q10: A computer program consists of two blocks written independently by two different

programmers. The block has an error with probability 0.2. The second block has an error with

probability 0.3. If the program returns an error, what is the probability that there is an error in

both blocks?