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COMP 10020
Lecturer: Dr. Saralees Nadarajah
Office: Room 2.223, Alan Turing Building
Email: [email protected]
COMP 10020 Example Classes
1. Mondays 4pm, LF15
2. Tuesdays 11am, LF15
3. Tuesdays 2pm, LF15
4. Fridays 12am, LF15
COMP 10020 Topics
1. Axioms of probability
2. Conditional probability and independence
3. Random variables
4. Some discrete distributions.
Example 1
A hat contains four slips numbered 1 to 4.
Two drawn without replacement:
Sample Space = ?
Axioms of Probability
0≤Pr(E)≤ 1
Pr(Sample Space) = 1
Pr(EUF) = Pr(E) + Pr (F) if E and F are mutually exclusive
Example 7
A bowl contains slips numbered 1,2,…, 20.
A slip drawn at random and its number noted:
Sample Space = ?
Pr(Number is Prime OR Divisible by 3) = ?
Example 8
The probability that a student passes mathematics is 2/3, and the probability that he passes biology is 4/9.If the probability of passing at least one course is 4/5, what is the probability that he will pass both courses?
Example 9
A bag contains 5 balls, 3 are red and 2 are yellow. Three balls are drawn without replacement. Describe the sample space.
Example 10
Let C be the event “exactly one of the events A and B occurs.” Express Pr (C) in terms of Pr (A), Pr (B) and Pr (A ∩ B).
Example 11
A six-sided die is loaded in a way that each even face is twice as likely as each odd face. All even faces are equally likely, as are all odd faces. For a single roll of this die find the probability that the outcome is less than 4.
Example 12
Is the following statement true: if A and B are mutually exclusive events then Pr (A ∩ B) = Pr (A) Pr (B). Justify your answer with a simple example.
Example 13
Anne and Bob each have a deck of playing cards. Each flips over a randomly selected card. Assume that all pairs of cards are equally likely to be drawn. Determine the following probabilities:
(a) the probability that at least one card is an ace,
(b) the probability that the two cards are of the same suit,
(c) the probability that neither card is an ace.
Example 14
A die is rolled and a coin is tossed, find the probability that the die shows an odd number and the coin shows a head.
Example 15
A six--sided die is loaded in a way that each even face is twice as likely as each odd face. All even faces are equally likely, as are all odd faces. For a single roll of this die find the probability that the outcome is less than 4.
Example 16
Out of the students in a class, 60% are geniuses, 70% love chocolate, and 40% fall into both categories. Determine the probability that a randomly selected student is neither a genius nor a chocolate lover.
Example 17
Is the following statement true: if A and B are mutually exclusive events then Pr (A ∩ B) = Pr (A) Pr (B). Justify your answer with a simple example.
Example 18
If Pr (A) = 0.5 and Pr (B) = 0.4,but we have no further information about the events A and B, how big might Pr (A U B) be? How small might it be? How big might Pr (A ∩ B) be? How small might it be?