TR1713 120142015
Assignment 1
1. In a certain company, 70% of employees know C++, 60% know Java and 50% know both
languages.
a)
b)
c)
d)
e)
If an employee knows C++, what is the probability that she also knows Java?
If an employee knows Java, what is the probability that she also knows C++?
If an employee knows at least one of these languages, what is the probability
that he knows both of them?
Are the events “knows C++” and ”knows Java” mutually exclusive?
Are the events ”knows C++” and ”knows Java” independent?
2. There are two boxes containing colored balls. The first box contains 50 red balls and 50
blue balls. The second box contains 30 red balls and 70 blue balls. One of the two boxes is
randomly chosen (both boxes have probability of being chosen) and then a ball is drawn
at random from one of the two boxes. If a red ball is drawn, what is the probability that it
comes from the first box? (Bayes’ Theorem)
3. An internet search engine looks for a certain keyword in a sequence of independent web
sites. It is believed that 20% of the websites contain this keyword. Out of the first 5
websites, let Y be the number of websites that contain the keyword.
a) Find the probability distribution of Y.
d) Compute the expected value and the standard deviation of Y.
e) Compute the probability that at least 2 websites contain the keyword.
4. The mean number of bacteria per milliliter of a liquid is known to be 4.
Assuming that the number of bacteria follows a Poisson distribution, find
the probability that, in 1ml of liquid, there will be
(a) no bacteria
(b) 4 bacteria
(c) fewer than 3 bacteria
Find the probability that
(d) in 3ml of liquid there will be less than 2 bacteria
(e) in 0.5ml of liquid there will be more than 2 bacteria
Submit on week 8th (After mid-break)