Tuesday 26 July 2011

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

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