# MTH4: PROBABILITY AND SET

## 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. 1. Example , Given that a die is thrown , find the probability of obtaining an even number. 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. 1. Probability of getting a number not 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 PROBABILITY   3. 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. 1. C is the event of obtaining an add a 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 Rule
Events where the occurrences of one doesn’t not effect the occurrence of the other are called independent events.

Example
I f two balls have to be picked randomly from a bag containing Red, blue and Yellow balls.
Events
A. 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.
Examples
1) 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) 1. If the first ball is not replaced . Find the ball first and a black ball second. Exercise
Write 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

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### ASSIGNMENT : PROBABILITY AND SET ASSIGNMENTMARKS : 30  DURATION : 3 hours

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