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## PROBABILITY

The set of all possible out come of an experiment is called the possibility space. (5)

Definition ; the probability of an event e.g (A) in a possibility space (5) consisting of a finite number of equally likely . Out comes denoted by P(A) is defined by the expression.

Note:0≤1

The probability of and event cannot be more than one and cannot go be less than zero.

b) Using example.

i) Find the probability of getting a number greater than 4.

Note:Given an event A e.g getting a number greater than four; the event “getting a number not great than four is denoted by A’/A*/A and P (A) + P(A’) = 1

2. Two ordinary dice are thrown , find the probability that a) a 2 is obtained.

b) Sum on the two dice is 3

c). Number on two dice are the same.

A VIDEO ABOUT THE INTRODUCTION TO PROBABILITY3. A counter is drawn from a box containing 10 red, is black , 5 green and 10 yellow. Counter find probability that the counter is

a). Black

b). Not green or yellow.

Note∶If A and B are any two events of the same experiment such that the probability

of P(A)= o and P(B)=0 .The P(A) or (B)

P(A or B)- p(A)+ P(B)- P(ANB)

P(Green or yellow=p(Green )+ p( Yellow)- P(Gn Y )

Given that a die is thrown , A is the event of obtaining an even number and B is the event that a prime number is obtained.

Find the probability of obtaining an even number or a prime number.

A and C are exhaustive the intersection is O; i.e they cannot occur at the same time; For example;

Given the first 10 number; A is the event that an even number smaller than 8 10 chosen and B is the event that an add number is chosen. If one number is picked at random, find the probability that A or B is obtained P(Au B)

∴The P(Au B) = P(A) + P(B) and this shows that A and B are said to be mutually exclusive event.

Multiplication RuleEvents where the occurrences of one doesn’t not effect the occurrence of the other are called independent events.

ExampleI f two balls have to be picked randomly from a bag containing Red, blue and Yellow balls.

EventsA. That a red ball is picked

B. That a blue ball is picked

C. That a yellow ball is picked.

D. All are independent events

In this case, the probability of events A and B i.e P (AnB) = p(A)X P(B) which is the multiplication rule for independent events.

Examples1) Given that a bag contains 5 red balls and 7 black balls. If a ball is drawn from the bag, the colour noted and the ball replaced .Then a second ball is drawn.

a) Find the probability that the first ball in red and the second is balck,

b) P(AnB) = P (A) x P(B)

ExerciseWrite the probabilities of these events A head resulting from tossing a coin.

The probability of anew car being detective in some way when it is delivered is almost

Approximately 2 cars

There are two sets of 10 counters numbered from 1 to 10. They drawn from each. What is the probability of scoring a total of 11 with the two counters.

6. A bag contains 5 red balls , 3 blue balls and 2 yellow balls. A ball is drawn and not replaced. A second ball is drawn. Find the probability of drawing:

i) Two red balls

ii) One blue ball and one yellow ball

iii) Two yellow balls.

Three students A , B, and C share shs. 240,000 in the ratio 7:5:3 . How much did

## Attachments38

## ASSIGNMENT : PROBABILITY AND SET ASSIGNMENT

MARKS : 30 DURATION : 3 hours

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