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` .
I have recently faced lot of problem while learning Dot Product Angle, But thank to online resources of math which helped me to learn myself easily on net.
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` .
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` .
I have recently faced lot of problem while learning Dot Product Angle, But thank to online resources of math which helped me to learn myself easily on net.
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` .
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