Understanding ‘Probability’: Beginners Guide

Probability simply means what is the likely hood that something will happen. The analysis of events governed by probability is called statistics. Let’s take a look at this topic in detail.

Introduction

The most common examples that are usually given to understand probability is that of flipping a coin and that of drawing a card; the first one being easier to understand as there are only two outcomes.

When flipping a coin, there are two possible outcomes – either you get a heads or you get a tails.

So what is the probability that the coin will landing on Heads when you flip it?

Some of you might say that the likelihood is half/half, or fifty percent.

In, Probability it is written as P(H) = 1/2 = 0.5.

P(H) = Likelihood that it will be Heads / Total number of outcomes.

In the case of throwing a dice, the probability that you will get a particular number is 1 in 6 i.e. 1/6.

Measuring Probability

Probabilities are measured on a scale between 0 and 1.
The sum of all probabilities associated with an experiment is 1.
P(Heads) + P(Tails) = 1/2 + 1/2 = 1
Probabilities are often presented as percentages. For example,
P(E) = 0.5 or 50%
P(E) = 0.75 or 75%
P(E) = 0.125 or 12.5%

Evaluating probabilities for discrete variables

For an event E associated with an experiment X, the probability of observing the event is denoted by P(E) and is defined as the following,
P(E) = Number of ways an event can occur / Total number of possible outcomes

Examples

Here are some more examples:

Q) Three cards are drawn from a well shuffled pack of 52 cards. Find:
i) The number of ways of drawing all three as number cards.
ii) The number of ways of drawing 2 heart cards and 1 ace cards.
iii) The probability of getting all the three cards as picture cards.

Answer:
i) In a deck of cards, there are 36 number cards,
n=36

3 cards are drawn, therefore r=3.

Choosing number cards = 36 C 3
= 36! / 3! (36-3)! = 36! / 3! (33)! = 36*35*34*33! / 3! (33)! = 36*35*34/3*2*1 = 7140 ways.

So there are 7140 ways of drawing number cards.

ii) There are 13 hearts and 4 ace cards.

We can select 2 heart cards C(13, 2) ways

We can select 1 ace card C(4,1) ways

so the answer = C(13, 2) * C(4,1) = 13!/2!(13-2)! * 4!/1!(4-1)! = 312 ways

There are 312 ways of drawing 2 heart cards and 1 ace cards.

iii) Sample space (S) = select 3 cards out of 52 cards.
n(s) = 52 C 3

The event(a) of getting a face card = 12 C 3
Probability of getting three picture cards = n(a)/n(s) = 12 C 3 / 52 C 3 = 220 / 22100 = 9.954

So probability of getting three picture cards = 9.954