MathematicsFA 3

GROUP-5

Topic:-PROBABILITY

Group MembersSonali, Sorav Punia, SUMIT RANA, Sumit Goswami & V.

Srividhaya.

PROBABILITY

PROBABILITYThe Greater the Probability the

more likely the event

will occur.

PROBABILITY

of any EVENT is between 0 and

1.

SUM of ALL Probabilities

of ANY event is 1.

Basic’s about Probability

IS THE

MATHEMATICSOF

CHANCE

HISTORY OF PROBABILITYPROBABILITY THEORY HAD ITS ORIGIN IN THE 16TH CENTURY

WHEN AN ITALIAN PHYSICIAN AND MATHEMATICIAN J CARDAN WROTE THE FIRST BOOK ON THE SUBJECT, THE BOOK ON GAMES OF CHANCE. SINCE ITS INCEPTION, THE STUDY OF PROBABILITY HAS ATTRACTED THE ATTENTION OF GREAT MATHEMATICIANS,

JAMES BERNOULLI (1654-1705), A. DE MOIVRE (1667-1754) AND PIERRE SIMON LAPLACE ARE AMONG THOSE WHO MADE

SIGNIFICANT CONTRIBUTIONS TO THE FIELD, LAPLACE’S THEORIE ANALYTIQUE DES PROBABILITIES, 1812, IS CONSIDERED TO BE THE GREATEST CONTRIBUTION BY A SINGLE PERSON TO THE

THEORY OF PROBABILITY. IN RECENT YEARS, PROBABILITY HAS BEEN USED EXTENSIVELY IN MANY AREAS SUCH AS BIOLOGY,

ECONOMICS, GENETICS, PHYSICS, SOCIOLOGY ETC.

MATHEMATICIAN LAPLACE

THEORITICAL ProbabilityNotation: The probability that Event E will occur is written P(E) and

is read “the probability of event E.” The Probability of an Event, E:

Consider a pair of DiceEach of the Outcomes in the Sample Space are random and equally

likely to occur.

P(E) =Number of Event Outcomes

Total Number of Possible Outcomes in S

e.g. P( ) =

(There are 2 ways to get one 6 and the other 4)18

1

36

2

The Complement

of Event E is the set of all outcomes in a

sample space that are

not included in Event E.

The Complement of event E is denoted by

Properties of Probability:

EorE

COMPLIMENTRY Event

)(1)(

)(1)(

1)()(

1)(0

EPEP

EPEP

EPEP

EP

)(1)(

)(1)(

1)()(

1)(0

EPEP

EPEP

EPEP

EP

FOR ANY EVENT:-

CARDSRED (26) BLACK (26)

OTHER CARD’S FOR ALL:- ACE,2,3,4,5,6,7,8,9,10

NOW LET’S TRY OUT SOME EXAMPLESQUE A Dice is thrown, then find out:-

ANSWER

ANSWER

Question :Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on (i) the same day? (ii) consecutive days? (iii) different days?

Question :A die is numbered in such a way that its faces show the number 1, 2, 2, 3, 3, 6. It is thrown two times and the total score in two throws is noted. Complete the following table which gives a few values of the total score on the two throws:

What is the probability that the total score is(i) even? (ii) 6? (iii) at least 6?

+ 1 2 2 3 3 6

1 2 3 3 4 4 7

2 3 4 4 5 5 8

2 3 4 4 5 5 8

3 4 5 5 6 6 9

3 4 5 5 6 6 9

6 7 8 8 9 9 12

Total number of possible outcomes when two dice are thrown = 6 × 6 = 36(i) Total times when the sum is even = 18P (getting an even number)

(ii) Total times when the sum is 6 = 4P (getting sum as 6)

(iii) Total times when the sum is at least 6 (i.e., greater than 5) = 15P (getting sum at least 6)

ANSWER

Question :A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, determine the number of blue balls in the bag.

Answer :Let the number of blue balls be x.Number of red balls = 5Total number of balls = x + 5P (getting a red ball)

P (getting a blue ball)

Given that,

However, the number of balls cannot be negative.Hence, number of blue balls = 10

Question :A box contains 12 balls out of which x are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball?If 6 more black balls are put in the box, the probability of drawing a black ball is now double of what it was before. Find x.

Answer :Total number of balls = 12Total number of black balls = xP (getting a black ball) =

If 6 more black balls are put in the box, thenTotal number of balls = 12 + 6 = 18Total number of black balls = x + 6

P (getting a black ball now)

According to the condition given in the question,

QUESTION . What is the probability that an ordinary year has 53 Sunday.

QUESTION. What is the probability that a leap year has 53 Sundays and 53 Mondays.

QUESTION. In a lottery of 50 tickets numbered 1 to 50, one ticket is drawn. Find the probability that the drawn ticket bears a prime number.

QUESTION. A bag contains 3 red balls, 5 blackballs and 4 white balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is

QUESTION. Ticket numbered from 1 to 20 are mixed up and a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 of 7?

QUESTION. In a lottery there are 10 prizes and 25 blanks. What is the probability of getting a prize?

QUESTION. A bag containing 4 red, 5 black and 6 white balls. A ball is drawn from the bag at random. Find the probability the ball drawn is ……

QUESTION. A bag contains cards which are numbered from 2 to 90. A card is drawn at random from the bag. Find the probability that it bears …..

QUESTION. A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the number 1,2,3,….12, What is the probability that it will point to ……

QUESTION. In a class, there are 18 girls and 16 boys. The class teacher wants to choose one pupil for class monitor. What she does, she writes the name of each pupil on a card and puts them into a basket and mixes thoroughly. A child is asked to pick one card from the basket. What is the probability that the name written on the card is ……

QUESTION. What is the probability that a number selected at random from the number 1,2,2,3,3,3,4,4,4,4, will be their average.

QUESTION. The probability of selecting a green mrable at random from a jar that contains only green, white and yellow marbles is ¼. The probability of selecting a white marble at random from the same jar is 1/3. if this jar contains 10 yellow marbles. What is the total number of marbles in the jar.

QUESTION. Find the probability that a number selected from the number 1 to 25 is not a prime number when each of the given number is equally likely to be selected.

QUESTION. A bag contains 6 red balls and some blue balls. If the probability of drawing a blue ball from the bag is twice that of a red ball, find the number of blue balls in the bag.

ACKNOWLEDGEMENT

THANK YOU !