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# Probability (Event And Outcome)

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 S1 = (1, 2, 3, 4, 5, 6) does not influence the outcome of the second throw. S2 = (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 1/52.

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:

(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.

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:

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.