Quick Study Notes on Probability - Part I

Remember points:

(1) Any value of probability is not more than – 1

O <  P (E) < 1

(2) Formulae of probability

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

Where: 

P(E) = Probability of an events.

n(E) = Total No. of required events.

n(S) = Total No. of possible events.

Probability divided into 4 parts

• Coin based problems
• Dice based problems
• Balls based problems
• Card based problems

1. Coin based problems:

I. Single – Coin

1. When a single coin throw at random them find the probability –

• a getting head
• a getting tell

1. Single coin are two face

{H, T} – Two events.

P (E) = n(E) / n(S)
= 1/2

1. 1/2 (Short Trick)

A getting – tail

2. 1/2

II. Double Coin

(1) Two coin are throw at random, then find the probability.

(i) A getting – Head

(ii) getting at least one head

(iii) both are head are getting

Solution:

4 events are required

Sample space – {HT< TH, HH, TT}

2\4 = 1\2

2. At least one head:

Events taken – {HT, TH, HH}

Þ 3/4

3. Both are Head

{HH}

Þ 1/4

No. of events – Short trick = 2ⁿ

Where n – no. of coin

2. Dice based problems:

I. Single dice:

When single dice throw at random find the probability that a getting even no.

Sample space: {1, 2, 3, 4, 5, 6}

Events : {2, 4, 6}

3/6 = 1/2 Þ Short trick

2. Double Dice 

When two dice thrown are random then find the probability that the sum on the top face of both the dice will be more than 9

Following are cases:

(5, 5) (6, 4) (4, 6) (6, 5) (5, 6) (6, 6)

So the total no. required events – 6

The total no. of possible events – 36

Hence probability – 6/36 = 1/6