1. An Introduction to Probability Theory

2. Simple Probability
Simple probability is defined as:

3. A probability of an event is certain to occur is 1 and the probability that an event cannot occur is 0.
If the probability of an event occurring is p, then the probability of this event not occurring is (1 – p)
E and E’ are Complementary Events

4. Probability (Possibility) Space
A number is selected at random from the set {2, 4, 6, 8} and another number is selected from the set {1, 3, 5, 7}. The two numbers are multiplied together. Draw a sample space diagram. 2 6 10 14 4 12 20 28 18 30 42 8 24 40 56 1 3 5 7

5. A bag contains 8 disks of which 4 are red, 3 are blue and 1 is yellow
A bag contains 8 disks of which 4 are red, 3 are blue and 1 is yellow. Calculate the probability that when one disk is drawn from the bag it will be:
a) Red
c) Blue
Answer:
Answer:
b) Yellow
d) Not blue
Answer:
Answer:

6. You can use Set notation when evaluating probabilities
Example:
One element is randomly selected from a universal set of 20 elements. Sets A and B are subsets of the universal set and n(A) = 15, n(B) = 10 and Find:
c) P(A’)
a) P(A)
Answer:
Answer: b) d)
Answer:
Answer:

7. A and B are subsets of the universal set and n(A) = 25, n(B) = 20, and there are 50 elements in the universal set. When one element is selected at random, calculate:
a) P(A)
c) P(B’)
Answer:
Answer: b) d)
Answer:
Answer:

8. A number k is chosen from {-3, -2, -1, 0, 1, 2, 3, 4}
A number k is chosen from {-3, -2, -1, 0, 1, 2, 3, 4}. What is the probability that the expression below can be written as a product of two linear factors, each with integer coefficients?
Answer:
A number c is chosen from {1, 2, 3, 4, 5, 6}. What is the probability that the expression below intersects the x-axis?
Answer:

9. a) Each letter is in the correct envelope
A secretary has three letters to put into envelopes. Being in a rush, she puts them in at random. Find the probability that:
a) Each letter is in the correct envelope
b) No letter is in its correct envelope.
Answers:
Two dice are rolled and the product of the scores is found. Find the probability that the product is:
a) odd
b) prime
Answers:

10. Two dice are rolled. Find the probability that:
Three people, A, B and C play a game which is purely determined by chance. Find the probability that they finish in the order ABC.
Answer:
Two dice are rolled. Find the probability that:
a) the total score is 10
b) the dice show the same number
Answers:

11. (a) two girls and two boys;
There are 30 students in a class, of which 18 are girls and 12 are boys. Four students are selected at random to form a committee. Calculate the probability that the committee contains
(a) two girls and two boys;
(b) students all of the same gender.
Answer:
(a)
(b)
SPEC06/HL1/15