Classical Definition of Probability

Q.

Two squares are chosen at random on a chess board. The probability that they have a side in common is

1. $\frac{1}{9}$

2. $\frac{2}{7}$

3. $\frac{1}{18}$

4. None of these

Q.

A coin is tossed three times. If X denotes the absolute difference between the number of heads and the number of tails then $P\left(X=1\right)$ is

1. $1/2$

2. $1/6$

3. $2/3$

4. $3/4$

Q.

In a single throw of two dice, find the probability of obtaining 'a total of $8$'.

Q.

There are 10 points in a plane no three of which are in the same straight line, excepting 4 points, which are collinear.

Find the probability that

(i) number of straight lines obtained from the pairs of these points.

(ii) number of triangles that can be formed with the vertices as these points.

Q.

Two dice are thrown. The probability that the sum of the number appearing is more than $10$ is

1. $\frac{1}{18}$

2. $\frac{1}{12}$

3. $\frac{1}{6}$

4. None of these

Q. In Class XI of a school 40% of the students study Mathematics and 30% study Biology. 10% of the class study both Mathematics and Biology. If a student is selected at random from the class, find the probability that he will be studying Mathematics or Biology.

Q.

If the odds against an event be $2:3$, then the probability of its occurrence is

1. $\frac{1}{5}$

2. $\frac{2}{5}$

3. $\frac{3}{5}$

4. $1$

Q. If 4-digit numbers greater than 5, 000 are randomly formed from the digits 0, 1, 3, 5, and 7, what is the probability of forming a number divisible by 5 when, (i) the digits are repeated? (ii) the repetition of digits is not allowed?

Q. 4 cards are drawn from a well-shuffled deck of 52 cards. What is the probability of obtaining 3 diamonds and one spade?

Q.

Three dice are thrown simultaneously. What is the probability of containing a total of $17$ or $18$

1. $\frac{1}{9}$

2. $\frac{1}{72}$

3. $\frac{1}{54}$

4. None of these

Q.

Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among the 100 students, what is the probability that.
(a) You both enter the same section?
(b) You both enter the different sections?

Q. A and B are events such that P(A) = 0.42, P(B) = 0.48 and P(A and B) = 0.16. Determine (i) P(not A), (ii) P (not B) and (iii) P(A or B).

Q. A letter is chosen at random from the word ‘ASSASSINATION’. Find the probability that letter is (i) a vowel (ii) an consonant

Q.

In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random, find the probability that (i) The student opted for NCC or NSS. (ii) The student has opted neither NCC nor NSS. (iii) The student has opted NSS but not NCC.

Q. A and B are two events such that P(A) = 0.54, P(B) = 0.69 and P(A ∩ B) = 0.35. Find (i) P(A ∩ B) (ii) P(A′ ∩ B′) (iii) P(A ∩ B′) (iv) P(B ∩ A′)

Q. Three coins are tossed once. Find the probability of getting (i) 3 heads (ii) 2 heads (iii) at least 2 heads (iv) at most 2 heads (v) no head (vi) 3 tails (vii) exactly two tails (viii) no tail (ix) at most two tails.

Q. In a lottery, person choses six different natural numbers at random from 1 to 20, and if these six numbers match with the six numbers already fixed by the lottery committee, he wins the prize. What is the probability of winning the prize in the game? [ Hint: order of the numbers is not important.]

Q. A coin is tossed twice, what is the probability that at least one tail occurs?

Q.

A four digit number is formed using the digits 0, 1, 2, 3, 4 without repetition. Find the probability that it is divisible by 4.

1. 5/16

2. 3/4

3. 1/4

4. 7/20

Q.

A bag contains 6 white, 7 red and 5 blue balls. Three balls are drawn at random. Find the probability of the event 'balls drawn are one of each color'.

1. 6/18

2. 35/136

3. 1/4

4. 35/172

Q. 1. A bag contains 25 cards numbered from 1 to 25. A card is drawn at random from the bag. Find the probability that the number on the card is : (i) divisible by 3 or 5 (ii) a perfect square number.

Q. A five digit number is chosen at random.The probability that all the digits are distinct and digits at odd place are odd and digits at even places are even is

1. $\frac{1}{25}$
2. $\frac{25}{567}$
3. $\frac{1}{37}$
4. $\frac{1}{74}$

Q. The probability that out of 10 persons, all born in April, at least two have the same birthday is

1. $noneofthese$
2. $\frac{{}^{30}{P}_{10}}{(30{)}^{10}}$
3. $1-\frac{{}^{30}{P}_{10}}{30!}$
4. $\frac{{30}^{10}{-}^{30}{P}_{10}}{{30}^{10}}$

Q.

Three digits are chosen at random from $1,2,3,4,5,6,7,8,9$ without repeating any digit. What is the probability that the product is odd?

1. $\frac{1}{2}$

2. $\frac{7}{48}$

3. $\frac{5}{42}$

4. $\frac{5}{108}$

Q. If E and F are events such that P(E) = , P(F) = and P(E and F) = , find:(i) P(E or F), (ii) P(not E and not F).

Q. A die has two faces each with number ‘1’, three faces each with number ‘2’ and one face with number ‘3’. If die is rolled once, determine (i) P(2) (ii) P(1 or 3) (iii) P(not 3)

Q. A die is thrown, find the probability of following events: (i) A prime number will appear, (ii) A number greater than or equal to 3 will appear, (iii) A number less than or equal to one will appear, (iv) A number more than 6 will appear, (v) A number less than 6 will appear.

Q. Eight players $P_1,P_2,\cdots ,P_8$ paly a knock - out tournament. It is known that whenever the players $P_{i}and{P}_j$ play, the player $P_i$ will win if i < j. Assuming that the players are paired at random in each round, what is the probability that the player $P_4$ reaches the final?

1. $\frac{3}{35}$
2. $\frac{4}{35}$
3. $\frac{1}{5}$
4. $\frac{12}{35}$

Q. A number x is chosen at random from the numbers -3, -2, -1, 0, 1, 2, 3. Find the probability of getting x sucn that \vert x\vert<2.

Q.

Out of 100 students, two sections of 40 and 60 students are formed, if you and your friends are among the 100 students. What is the probability that

(i) you both enter the same section?

(ii) you both enter the different section?