**DEFINITION OF TERMS**

(i)**Event**: When an experiment is performed two or more results or outcomes will be expected to happen. Each attempt is called a trial and the outcome of a trial and the outcome of a trial is called an event, usually denoted by E.

(ii)**Random Experiment**: A random experiment is a repetitive process which may result in any one of the possible outcomes of the experiment OR:

(iii)**Sample space**: The sample space of a random experiment is the set containing all the possible outcomes of the experiment OR:

Sample space is all the possible outcomes of a trail in an experiment usually denoted by S.

(iv)The number of the points in a sample space n(s), and in an event, E is n(E).

**Examples**

1. When a coin is tossed twice, all the possible outcomes i.e. the sample space

S = {HH, HT,TH, TT}

\ n(s) = 4

2. If a die is cast once, there are six outcomes.

\ the sample space , S = {1, 2, 3, 4, 5, 6}

\ n(S) = 6

Suppose an event E that an even number is thrown,

then E = {2, 4, 6} and n(E) = 3.

3. A box contain 16 red, 6 white, and 18 blues balls.

The sample spaces, S = {16 + 6 + 18) balls

n (S) = 40

4. When a die is tossed twice, the outcome of the first toss S^{1} = (1, 2, 3, 4, 5, 6) does not influence the outcome of the second throw. S^{2} = (1, 2, 3, 4, 5, 6). The two outcomes are independent of each other. For instance, the chance of throwing a5 in the first toss is ^{1}/_{6} does not influence the chance of the throw of 2 in the second toss (i.e. ^{1}/_{6}); they are Independent Event.

**Equally likely events:** Two or more events are said to be equally likely to happen if the chance of occurrence of each of the same.**e.g.**

1.In the throw of a die, there are six equally likely outcomes, S = {1, 2, 3, 4, 5, 6} the change of each occurring is 1 out of 6 c.c. ^{1}/_{6}.

2.From a pack of 52 cards, the chance of picking any of the cards at random is ^{1}/_{5}2.

**PROBABILITY**

The probability of an event is the chance of its occurrence, that is the likelihood of the event happening with respect to the sample space.

Prob. Of E = (number of elements in E) / of total elements in S

\P(E) = n(E) / n(S)

**NOTE**: Probability of an event lies between 0 and 1 i.e. O<P(E) <1

then the prob. that it will not occur is 1 – P(E).

EVALUATION

1. In a class of 27 boys and 12 girls, what is the probability of picking a girl.

2. A no is chosen at random from 40 to 50, find the probability that it is a prime number.

3. If all 2-digits numbers 00, 01, 02, …….99 are equally likely to be chosen, find the probability that a number picked at random has 5 as its first digit.

**EVALUATION**

Use the figure below to answer the following:

16 | 2 | 3 | 13 |

5 | 11 | 10 | 8 |

9 | 7 | 6 | 12 |

4 | 14 | 15 | 1 |

(a) If a number is picked at random from the figure. What is the probability that it is:-

(i) Odd (ii) Prime (iii) even (iv) less than 10

(v) Exactly divisible by 3 (vi) a perfect square (vii) a perfect cube?

(b) If a row or column is picked at random from the figure. What is the probability that the total of its no is(i) 34 (ii) 35

**GENERAL EVALUATION**

1 A bag contains black balls, 3 green balls and 4 red balls, A ball is picked form the bag at random, what is the probability that it is

(a) Black (d) yellow (c) Green (d) not black (d) either black ore red

2 A school contains 357 boys and 323 girls, if a student is chosen at random, what is the probability that a girl is chosen.

**READING ASSIGNMENT**

NGM SSS2, page113-114, exercise11a, numbers 1-12.

**WEEKEND ASSIGNMENT**

**OBJECTIVE**

1 What is the probability of throwing a number greater than 4 with a single fair die.

(a) ½ (b) 1/3 (c) 5/6 (d) 2/3

2 A number is chosen at random from the set (11, 12, 13, ….25) what is the probability that the number is odds?(a) 7/15 (b) 8/15 (c) 1/4 (d) 3/4

3 A box contains 8 blues 6 yellow and 10 green balls , one all is picked at random from the box, what is the probability that the ball is yellow. (a) 1/3 (b)½ (c) 3/4 (d) 5/12

4 A coin is tossed twice, what is the probability of obtaining at least a head

(a) 3/4 (b) 1/3 (c) 2/5 (d) 1/2

5 A letter is chosen at random from the word PROBABILITY, what is the probability that the letter is a vowel? (a) 3/11(b) 4/11 (c) 5/11 (d) 6/11

**THEORY**

1 Two groups of male students X and Y cast their votes in an election of an officer; he results are as shown in the table below:

In favour | Against | ||

Group X | 152 | 48 | 200 |

Group Y | 88 | 62 | 150 |

240 | 110 |

a. How many students participate in the election?

b. If a student in favour of the officer is selected, what is the probability that he is from group X?

c. A student is choosen at random, what is the probability that he is against the officer?

2 A ltter is choose at random from 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 of NIGERIA.

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