TOPIC 2: Probability

PROBABILITY:

INTRODUCTION PROBABILITY

 Probability is a branch of mathematics that deals with calculating the likelihood of a given event's occurrence, which is expressed as a number between 1 and 0.

An event with a probability of 1 can be considered a certainty: for example, the probability of a coin toss resulting in either "heads" or "tails" is 1, because there are no other options, assuming the coin lands flat.

An event with a probability of .5 can be considered to have equal odds of occurring or not occurring: for example, the probability of a coin toss resulting in "heads" is .5, because the toss is equally as likely to result in "tails." An event with a probability of 0 can be considered an impossibility: for example, the probability that the coin will land (flat) without either side facing up is 0, because either "heads" or "tails" must be facing up. A little paradoxical, probability theory applies precise calculations to quantify uncertain measures of random events.

FORMULA:

The formula for probability tells you how many choices you have over the number of possible combinations.

Example 1:

Suppose a coin is flipped 3 times. What is the probability of getting two tails and one head?

Solution: For this experiment, the sample space consists of 8 sample points.

S = {TTT, TTH, THT, THH, HTT, HTH, HHT, HHH}

Each sample point is equally likely to occur, so the probability of getting any particular sample point is 1/8. The event "getting two tails and one head" consists of the following subset of the sample space.

A = {TTH, THT, HTT}

The probability of Event A is the sum of the probabilities of the sample points in A. Therefore,

P(A) = 1/8 + 1/8 + 1/8 = 3/8

**In this case,you can use a tree diagram to look at which is getting two tails and one head faced coin.

Example 2:

Two dice are thrown together.
Use a tree diagram to find the probability that one number is even and the other is odd.

There are six possible scores on one die: {1, 2, 3, 4, 5, 6}
Of these, three are even: {2, 4, 6} and three are odd: {1, 3, 5}

The tree diagram look like this..

So the probability that one number is even and the other is odd



 Example 3:

 A man goes to work either by bus. The probability of bring late for works is 0.6 if he travals in two successive days.

a) find the probability that he will be late 

i) (L & L1)  
0.6 X 0.6
=0.36 

II) On exactly one of the two days
(L & L1) or (L1 & L)
(0.6 X 0.4) + (0.4 X 0.6)
0.24 + 0.24
= 0.48   

This are the 3 question if you wanna try..


Question 1

A bag contains 3 red balls, 2 green balls, and 1 blue ball. A ball is chosen at random and then placed back in the bag. A second ball is then chosen at random.

Find the probability that:
a. The first ball is red
b. The second ball is red
c. Both balls are red
d. The first ball is red and other is yellow

Question 2

A packet contains a large number of flower seeds which look identical, but produce flowers with one of the three colors; white, yellow and red. One half of the seeds produce white flowers and one third produce yellow flowers. The remainder of the seeds produce red flowers.

a. Find the probability that a particular seed will produce a red flower.
b. Find the probability that a particular seed will produce a flower that is not yellow.


Question 3

A glass jar contain 6 red, 5 green, 8 blue and 3 yellow marbles. if a single marble is chosen at random from the jar, what is the probability of choosing a red marble? a green marble? a blue marble? a blue marble? a yellow marble?