# Probability – Basic Concepts with Examples

Probability

Today we will discuss Topic – Probability Basic Concepts with Examples

I. Experiment – The process of rolling dice is known as experiment.

II. Random Experiment – The process of rolling dice randomly is known as Random experiment.

• Rolling an unbiased dice
• Tossing a fair coin
• Drawing a card from a pack of well shuffled cards.
• Picking up a ball of certain colour from a bag containing balls of different colours.

III. Sample Space – The set of total possible outcomes in an random experiment is known as sample space, denoted by S.

• For a dice S = {1, 2, 3, 4, 5, 6}
• For a coin S ={H, T}
• If two coins are tossed, then

S = {HH, HT, TH, TT}

IV. Event – Any subset of a sample space is called an event, denoted by E.

In the above, E = {2, 4, 6} is and event.

V. Probability of occurrence of an event-

Where,

n(E) = Total number of required outcomes.

N(S) = Total number of possible outcomes.

P(E) = Probability of Events.

Example –

For rolling a dice

Probability of even number = 3/6                  n(E) = {2, 4, 6}

n(S) = {1, 2, 3, 4, 5, 6}

P(E) = 1/2

Results –

Coins

Example 1

Find the probability of head when single coin is tossed.

Solution –

For single coin

n(E) = 1 {H}

n(S) = 2 {H, T}

P(E) = 1/2

Example 2 –

Find the probability of 1 head when two coins are tossed simultaneously.

Solution –

For two coins

n(S) = 4{(H, H) (T,T) (H,T) (T,H)}

n(E) = 2{(H,T) (T,H)}

P(E) = 2/4 = 1/2

Example 3 –

Find the probability of at least one head when two coins are tossed simultaneously.

Solution –

For two coins

n(S) = 4{(H,H) (T,T) (H,T) (T,H)}

Here n(E) = 3{(H,H) (H,T) (T,H)}

P(E) = 3/4

Dice

Example 1 –

Find the probability of getting a multiple of 3 when one dice is thrown once.

Solution –

n(S) = 6            {1, 2, 3, 4, 5, 6}

n(E) = 2             {3, 6}

P(E) = 2/6 = 1/3

Example 2 –

Find the probability of that number which is multiple of 2 when one dice is thrown once.

Solution –

Balls/ Marbles

Example 1 –

A box contains 5 red, 4 green & 6 black balls. If 3 balls are drawn at random.

(i) Find the probability that all balls are red colour.

Solution –

(ii) Find the probability that 1 ball is red and 2 balls are green.

Solution –

(iii) Find the probability that none ball is red.

Solution –

(iv) Find the probability that at least one ball is red.

Solution –

P (at least 1 red) = 1 – (none red)

= 1 – 24/91 = 67/91

Example 2 –

A bag contains 6 white balls and 4 black balls. 2 balls are randomly taken away. Find the probability that they are of the same colour.

Solution –

Example 3 –

A box contains 4 black, 3 red and 2 yellow balls. Two balls are drawn at randomly. What is probability that they are not of the same colour?

Solution –

Cards

2, 3, 4, 5, 6, 7, 8, 9, 10 – number of cards      9 × 4 = 36

Ace, King, Queen, Jack – Honour cards       4 × 4 = 16

Example 1 –

If from a pack of 52 cards, 1 card is drawn at random. Find the probability that the card is an Ace card.

Solution –

Example 2 –

If from a pack of 52 playing cards, 1 card is drawn at random. What is the probability that it is either a king or queen?

Solution –

With this we will finish this topic here.