MTH4: PROBABILITY AND SET

This unit is about probability which is the measure of the likeliness that an event will occur.

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.

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  1. Example , Given that a die is thrown , find the probability of obtaining an even number.

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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.

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  1. Probability of getting a number not greater than 4

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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


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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.

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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 )

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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.

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  1. C is the event of obtaining an add a number.

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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)

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∴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)

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  1. If the first ball is not replaced . Find the ball first and a black ball second.

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

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

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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.

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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.

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

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ASSIGNMENT : PROBABILITY AND SET ASSIGNMENT MARKS : 30  DURATION : 3 hours

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