Probability

Sample Space

Sample Space is the collection of all possible outcomes of an experiment.

In coin tossing experiment, sample space is {H , T}.

In dice throwing experiment, sample space is {1, 2, 3, 4, 5, 6}.

Probability

Probability is the likelihood or chance of an event occurring.

Probability is a number between 0 and 1.

The probability of a sure event is 1.

The probability of an impossible event is 0.

Probability = Number of favourable events / Total number of events

When rolling a dice, total number of events is 6

P (getting a 3 when rolling a dice) = 1/6

P (getting an even number when rolling a dice) = 3/6 = 1/2

P (getting a number larger than 2 when rolling a dice) = 4/6 = 2/3

P (getting a number smaller than 7 when rolling a dice) = 6/6 = 1

P (getting a number larger than 6 when rolling a dice) = 0/6 = 0

An alphabet is selected at random from the word infocom. Find the probability of selecting

(i) a vowel (ii) a consonant.

There are 7 alphabets in the word infocom.

3 vowels – i, o, o.

4 consonants – n, f, c, m.

(i) P (selecting a vowel) = 3/7

(ii) P (selecting a consonant) = 4/7

Questions

1. A box has 25 cards, 10 of them are Red Colour and the rest are Blue Colour. A card is picked at random from the box. Find the Probability that it is a Red card.

2. A box has 10 English, 15 Chinese and 5 Malay books. A book is picked at random from the box. Find the Probability that it is a (a) Chinese Book (b) non-English book.

3. A number is picked at random from 2,3,4,5,6,7,8,9. Find the probability that it is (a) a prime number (b) an even number (c) a multiple of 3 (d) greater than 5.

4. A class has 15 boys and 6 of them wear spectacles. The class also has 12 girls and 5 of them wear spectacles. Find the probability of selecting a (a) boy (b) girls (c) student who wear spectacle (d) girl who do not wear spectacle.