__Probability__

Experimental probability = No of required outcomes / No of possible outcomes

Ex 1 A die is rolled 200times. The outcomes obtained are as shown below

Number | 1 | 2 | 3 | 4 | 5 | 6 |

No. of times | 25 | 30 | 45 | 28 | 40 | 32 |

find the probability of obtaining a

- a) 2 b) 5 c) 6
- a) Probability of obtaining 2 is

= = O.15

- b) Probability of obtaining a 5 is

=

- c) Probability of a 6 is

=

__Theoretical Probability__

Theoretical probabilities are exact values which can be calculated by considering the physical nature of the given situation.

For Instance, the given situation for instance, the probability of getting a when a fair six-sided die is thrown is 1/6. Since any one of the six faces is equally likely. This is an example of theoretical probability.

Ex 2: Jessie throws a fair six-sided die what is probability that she throws a1) 4 9 (b) a4 (c) a number greater than 2 (d) an even number (e) either 1,,2,3,4,5,or 6.

__Solution__

- a) Since the faces of six- sided die are numbers 1-6

It is impossible to throw a 9

Probability +0

(b) Probability of a 4 = no of required outcome

no of possible outcome

= 1/6

(c) There are 4 numbers greater than 2

Prob. (a no greater than 2) = 4/6 = 2/3

(d) No of even numbers =3

P (an even number) = 3/6 = ½

(e) P(Either 1, 2,3,4,5 or 6) =

Note: If P is the probability of an event happening then p lies in the range o<

the probability of an event not happening is 1 – P.

Ex. 3. A letter is chosen at random from the alphabet. Find the probability that it is 9a) F (b) F or T (c) one of the letters of the word FREQUENCY (d) Not one of the letters of the word Table.

__Solution__

- a) no. of f in alphabet = 1

p (F) = 1/26

- b) P ( F or T) = p(f) +p (T)

+ = =

(c) No.of letters in the word FREQUENCY = 8

p(one of letters in the word FREQUENCY= =

- d) no.. of letters in the word TABLE = 5

p(one of letters in the word TABLE) = 5/26

p(not one of the letters in the word TABLE) =1-5/56

=21/26

**Note:** ‘At random’ means in a free, irregular way

__Exercises__

- A statical survey shows that 28% of all men take size 9 shoes. What is the probability that your friend’s father takes size 9 shoes?

Solution

prob (that a person takes size 9 shoes) =

- A school contains 357 boys and 323 girls If a student is chosen at random, What is the probability that a girl is chon?

Solution

No. of girls =323

Total no. of students = 323 + 357 =680

p (a girl is chosen) = 323 =193

680 40

- A letter is chosen at random fro m the alphabet. Find the probability that it is
- a) M
- b) not A or Z
- c) either P,Q,R or S
- d) one of the letters

__Solution__

n(alphabets) =26

- a) no. of m in the alphabets = 1

P(M) = 1/26

P (A) = 1/26

P(A or Z) =

P( not A or Z) = 1

- c) P (either P,Q,R or S) =
- d) P (one of the letters of Nigeria) =

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