Probability I

7.1    Sample Space

An experiment is a process or an operation with an outcome.

E.g.  1

Toss a balanced dice once and observe its uppermost surface

E.g.  2
 When a coin is tossed, we can only get 2 results :

Ø  Head                      

Ø  Tail                      

The set of all possible outcomes of an experiment is called a sample space.  It is usually denoted by S.

E.g.  3

En. Adam has a fruit stall.  He sells bananas, apples, watermelons, papayas and durians.  Students of 4KP were asked to select their favourite fruit from the variety of fruits sold at En. Adam’s stall.

S = { bananas, apples, watermelons, papayas, durians }

E.g.  4

A month is randomly selected from a year.  Describe the sample space of this experiment by using set notation.

S = { January, February, March, April, June, July, August, September, October, November, December }

7.2    Event

- Is a subset of the sample space.

- Is an outcome or a set of outcomes that satisfies certain conditions. 
- Denoted by a capital letter.

E.g.  1

A box contains five cards written with 1, 2, 3, 4 and 5 respectively.  A card is picked randomly from a box.

S = { 1, 2, 3, 4, 5 }

If we define just “the card with even numbers”, the outcome of J in set notation will be
J = { 2, 4 }

E.g.  2

A letter is randomly selected from the word “COMPUTER”.  Determine the number of the possible outcomes of the event that the selected letter is.

        i.            A vowel

      ii.            A consonant

Solution :

Let A = event that the selected letter is a vowel = { O, U, E }
Therefore, n (A) = 3

Let B = event that the selected letter is a consonant = { C, M, P, T, R }
Therefore, n (A) = 5

7.3    Probability of an Event

Probability of an event E,

- P (E) = ___number of outcomes of the event___
              number of outcomes of the sample space

- P (E) = n (E)
                        n (S)

- 0 ≤ P (E) ≤ 1

- P (E) = 0 means that it is impossible for the event to happen.

- P (E) = 1 means that the event is certain to happen.

- The closer the probability of a given event is to 1, the more likely it is to happen.

E.g.  1

A bag contains 3 red balls and 4 white ones.  If Rashid puts his hand in the bag and picks a ball, what is the probability that the ball he picked is white?

Solution :

S = { R1, R2, R3, W1, W2, W3, W4 }
n (S) = 7

Let E is the event of drawing a white ball
E = { W1, W2, W3, W4 }
n (E) = 4

Therefore, the probability of drawing a white ball is :          4
                                                                                        7

By Melissa Teh