3 P , i.e., (

P , i.e., ( ! ! = × × = sample points, each with a probability of . (a) A, B and C finish first, second and third, respectively.

There is only one finishing order for this, i.e., ABC. Thus P(A, B and C finish first, second and third respectively) = . (b) A, B and C are the first three finishers. There will be !

arrangements for A, B and C. Therefore, the sample points corresponding to this event will be ! in number. So P (A, B and C are first three to finish) !

Miscellaneous Exercise on Chapter . A box contains red marbles, blue marbles and green marbles. marbles are drawn from the box, what is the probability that (i) all will be blue? (ii) atleast one will be green?

. cards are drawn from a well – shuffled deck of cards. What is the probability of obtaining diamonds and one spade? PROBABILITY .

A die has two faces each with number ‘ ’, three faces each with number ‘ ’ and one face with number ‘ ’. If die is rolled once, determine (i) P( ) (ii) P( or ) (iii) P(not ) . In a certain lottery , tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy (a) one ticket (b) two tickets (c) tickets.

. Out of students, two sections of and are formed. If you and your friend are among the students, what is the probability that (a) you both enter the same section? (b) you both enter the different sections?

. Three letters are dictated to three persons and an envelope is addressed to each of them, the letters are inserted into the envelopes at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope. .

A and B are two events such that P(A) = . , P(B) = . and P(A ∩ B) = . .

Find (i) P(A ∪ B) (ii) P(A ´ ∩ B ´ ) (iii) P(A ∩ B ´ ) (iv) P(B ∩ A ´ ) . From the employees of a company, persons are selected to represent them in the managing committee of the company. Particulars of five persons are as follows: S. No.

Name Sex Age in years . Harish M . Rohan M . Sheetal F .

Alis F . Salim M A person is selected at random from this group to act as a spokesperson. What is the probability that the spokesperson will be either male or over years? .

If -digit numbers greater than , are randomly formed from the digits , , , , and , what is the probability of forming a number divisible by when, (i) the digits are repeated? (ii) the repetition of digits is not allowed? . The number lock of a suitcase has wheels, each labelled with ten digits i.e., from to .

The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase? MATHEMATICS Summary In this Chapter, we studied about the axiomatic approach of probability. The main features of this Chapter are as follows: