Probability Maths

Introduction to probability maths:

Probability is a word that is been used commonly in our day today life without going into the details of its actual meaning. We come across statements like:

(i) Probably it may rain to day.

(ii) He may possibly join politics.

(iii) Argentina team has good chance of winning world cup.

(iv) She is probably right.

In these kinds of statements, we generally use the terms: possible, probable, chance, likely etc. All these terms convey the same meaning that the event is not certain to take place or, or other words there is uncertainty about the occurrence of the event in question.

Now let us see few problems of this kind..


Example problems on probability maths:


1. Find the probability that a leap year selected at random will contain 53 Sundays.

Soln: We know that in a leap year there are 366 days.

They can be written as, 366 days = 52 weeks and 2 days.

Thus a leap year has always 52 Sundays.

The remaining two days cane as follows:

(i) Sunday and Monday

(ii) Monday and Tuesday

(iii) Tuesday and Wednesday

(iv) Wednesday and Thursday

(v) Thursday and Friday

(vi) Friday and Saturday

(vii) Saturday and Sunday.

Clearly, there are seven events are associated with this random experiment. Let X be the event that a leap year has 53 Sundays. This is possible if the last two days are either Sunday and Monday or Saturday and Sunday.

Therefore the required probability is `2/7` .

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More example problems on probability maths


2. Let X and Y throw a pair of dice. If X throws 9, find Y’s chance of throwing a higher number.

Soln: To throw a value greater than 9, we have the following possibilities:

{(4,6),(5,5),(5,6),(6,4),(6,6),(6,6)}. Therefore, the number of chances is 6.

When two dice are thrown, the total possibility is 36.

Hence the required probability is `6/36 = 1/6` .

3. A letter is chosen at random from the letters of the word “ASSASSINATION”. Find the probability that the letter chosen is a consonant.

Soln: The word “ASSASSINATION” has 13 words.

Here the consonants are {s, s, s, s, n, t, n}. Hence we have 7 consonants.

Therefore the probability to get a consonant is `7/13` .

Solving Probability Practice

Introduction to Probability:
Numerical measure of the likelihood of an event to occur is called as Probability. The probability should be a range in between 0 and 1.For solving probability practice problems we must know the following formula,

Probability of an event   =    number of times an event occurs / total number of outcomes

Consider an observation with 'n' possible ways and out of them in 'm' ways if the event 'A' occurs,then the probability of occurrence of the event 'A' is given by P(A) = m/n.

Let us workout some practice problems on solving probability in the following sections.

I like to share this Probability Problems and Solutions with you all through my article.

Probability on a coin problem:


Here Tossing a coin is a random experiment. When you toss a coin, you may get head or tail.Let us see how to  solving the coin problem.

1: What is the probability of getting Head when you toss a coin?

We can have 2 out-comes for tossing a coin :  Head or tail.

Here the event is getting Head. So we have 1 head.

So probability of getting head is one out of two outcomes.

Probability of getting Head    = number of head event occurs / total number of outcomes

= 1/2

= 0.5

So the probability of this practice problem is 0.5


Probability on Card problem:


In 52 cards, there are 13 spades, 13 clovers, 13 diamonds and 13 hearts , 26 cards are red in color (diamonds and heart) and 26 are black (spade and clover).Let us see how to  solving the card problems.

(1)  What is the probability that you get a red card?

The event is getting a red card. There are 26 red cards.

Total sample spaces are 52(52 cards).

Probability of getting a red cards = number of red cards / sample space

= 26/52

=1/2

= 0.5

(2) What is the probability of getting a spade when you draw from a well shuffled pack of 52 cards?

Number of Spade cards = 13

Total Sample space       = 52

Probability of getting a spade card = number of spade / total sample space

= 13/52

= 1/4

= 0.25

(3) What is the probability of getting a black queen in a pack of 52 cards?

In a pack of 52 cards, there are 2 Black Queens (spade 1, clover 1)

Total Sample space = 52

Probability of getting a black queen = number of black queen / total sample space

= 2/52

= 1/26

= 0.04

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Practice Problem:


The following practice problems on solving probability will helps for good understanding.

Practice problem 1: What is the probability of getting Tail when you toss a coin?

Practice problem 2: What is the probability of getting a diamond when you draw from a well shuffled pack of

52 cards ?

Answer key:

Practice problem 1:  0.5

Practice problem 2: 0.25