Topic 7: Probability & Exercise

PROBABILITY

 Definition of probability..

- Probability is a branch of mathematics that deals with calculating the likelihood of a given event's occurrences which is expressed as a number between 1 and 0. An event with a probability of 1 can be considered a certainty while an event with a probability of 0 can be considered an impossibility.

 

Calculating probabilities in a situation like a coin toss is straightforward, because the outcomes are mutually exclusive, either one event or the must occur. Each coin toss is an independent event. The outcome of one trial has no effect on subsequent ones. 

STEP TO FIND THE PROBABILITY 

STEP 1: LIST THE OUTCOME OF EXPERIMENT

STEP 2: COUNT THE NUMBER OF POSSIBLE OUTCOME OF THE EXPERIMENT

STEP 3: COUNT THE NUMBER OF FAVORABLE OUTCOMES 

STEP 4: USE THE PROBABILITY FORMULA.

Formula to find probability

p (a) = number of favorable outcomes / total number of possible outcomes

Example 1:

In a restaurant 40% of the male customers choose chicken for their main course. if a male customers choose chicken, the probability that he will choose ice cream to follow is 0.6 if he does not have a chicken the probability that he will choose ice cream is 0.3

complete the tree diagram to illustrate this information.

a) chicken and ice cream?

p (c & i) = p (0 x p(i)

= 0.4 x 0.6

= 0.24


b) ice cream only

p (c) = p (c) x p (1)

= 0.18

Example 2:

Box a contains 3 coins numbered 3, 5 and 7. Box b contains coins numbered 4, 6 and 8 respectively A coin is drawn randomly from box A and another coin is drawn from the box B. 

a)from the above,

i) 7 

solution:

= P( 3&4)

= 1/3 X 1/3

=1/9 

II) 13

solution:

(1/3 + 1/3) x (1/3 + 1/3)

= 2/9 x 2/9

= 4 / 81

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 is an example video of solving the probability. Let's learn from this video 😀

 Exercise

1) 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? 

 2) A single 6 sided die is rolled. what is the probability of each outcome? what is the probability of rolling an even number? of rolling an odd number?

  3) A number from 1 to 11 is chosen at random. What is the probability of choosing an odd number?

a) 1 / 11

b) 5 / 11

c) 6 / 11

d) None of the above