Chapter 2

If \(P(A)=0.42, P(B)=0.48\) and \(P(A \cap B)=\) \(0.16\), calculate the following: (i) \(P(\operatorname{not} A)\) (ii) \(P(\operatorname{not} B)\) (iii) \(P(A \cup B)\)

A committee consists of 9 experts taken from 3 institutions \(A, B\) and \(C\); of which 2 are from \(A, 3\) from \(B\) and 4 from \(C\). If 3 experts resign, then the probability that they belong to different institutions is (a) \(1 / 729\) (b) \(1 / 24\) (c) \(1 / 21\) (d) \(2 / 7\)

Two dice are thrown simultaneously. Find the probability of getting:(i) a total of at least 10 [CBSE-92] (ii) a doublet of even number. [HSB-9I(C)]

In a bag there are 5 white and 10 black balls. If ball is drawn at random from it, what is the probability that it is white?

Five-digit numbers are formed using the digits \(1,2,3,4,5,6\) and 8 . What is the probability that they have even digits at both the ends? (a) \(2 / 7\) (b) \(3 / 7\) (c) \(4 / 7\) (d) None

Two dice are thrown simultaneously. Find the probability of getting: (i) a multiple of 2 on one dice and a multiple of 3 on the other dice. [HSB-93 (C)] (ii) the same number on both dice. [HSB-90] (iii) a multiple of 3 as the sum. [CBSE-95]

The chance of throwing a total of 7 or 12 with 2 dice is (a) \(2 / 9\) (b) \(5 / 9\) (c) \(5 / 36\) (d) \(7 / 36\)

A coin is tossed twice. If the second throw results in a tail, a die is thrown. Describe the sample space for this experiment. \(\quad\) [CBSE-93]

In a lottery there are 90 tickets numbered 1 to \(90 .\) Five tickets are drawn at random. The probability that 2 of the tickets drawn are numbers 15 and 89 is: (a) \(\frac{2}{801}\) (b) \(\frac{2}{623}\) (c) \(\frac{1}{267}\) (d) \(\frac{1}{623}\)

An urn contains 7 red and 4 blue balls. Two balls are drawn at random with replacement. Find the probability of getting: [CBSE-2007] (i) 2 red balls. (ii) 2 blue balls. (iii) 1 red and 1 blue ball.

If \(P(A)=2 / 3, P(B)=1 / 2\) and \(P(A \cup B)=5 / 6\) then events \(A\) and \(B\) are (a) mutuallye xclusive (b) independent as well as mutually exclusive (c) independent (d) dependent only on \(A\)

Two dice are thrown simultaneously. Find the probability of getting: (i) an even number as the sum. [CBSE-95] (ii) the sum as a prime number. [CBSE-95]

From 80 cards numbered 1 to 80,2 cards are selected randomly. The probability that both the cards have the numbers divisible by 4 is given by: (a) \(21 / 316\) (b) \(19 / 316\) (c) \(1 / 4\) (d) None of these

Four coins are tossed simultaneously. Find the chance to get at least one head. [MP-1993]

Three coins are tossed simultaneously. List the sample space of the random experiment. [CBSE-91]

Fifteen persons among whom are \(A\) and \(B\) sit down at random at a round table. The probability that there are 4 persons between \(A\) and \(B\) is (a) \(1 / 3\) (b) \(2 / 3\) (c) \(2 / 7\) (d) \(1 / 7\)

\(A\) and \(B\) are two events such that \(P(A)=\) \(0.42, P(B)=0.48\) and \(P(A B)=0.16\), find \(P(A+B)\) [MP-1998]

Find the probability that the two digit number formed by digits \(1,2,3,4,5\) is divisible by 4 (while repetition of digit is allowed): (a) \(1 / 30\) (b) \(1 / 20\) (c) \(1 / 40\) (d) \(1 / 5\)

Find the probability of drawing a diamond card in each of the two consecutive draws from a well-shuffled pack of cards, if the card drawn is not replaced after the first draw. [CBSE-2002(C)]

When an ordinary dice is thrown find the probability of getting a number greater than 3 . $$ [\mathrm{MP}-93,97,2002,2004(A)] $$

The probability that at least one of the events \(A\) and \(B\) occurs is \(3 / 5\). If \(A\) and \(B\) occur simultaneously with probability \(1 / 5\), then \(P\left(A^{\prime}\right)+\) \(P\left(B^{\prime}\right)\) is (a) \(2 / 5\) (b) \(4 / 5\) (c) \(6 / 5\) (d) \(7 / 5\)

In four schools \(B_{1}, B_{2}, B_{3}, B_{4}\) the percentage of girls students is \(12,20,13,17\), respectively. From a school selected at random, one student is picked up at random, and it is found that the student is a girl. The probability that the school selected is \(B_{2}\) is (a) \(\frac{6}{31}\) (b) \(\frac{10}{31}\) (c) \(\frac{13}{62}\) (d) \(\frac{17}{62}\)

Two dice are thrown simultaneously. Find the probability of getting a sum 9 in a single throw. $$ \text { [MP-98, 2003, 2004 (C)] } $$

From a pack of 52 cards 2 cards are drawn in succession one by one without replacement. The probability that both are aces is (a) \(2 / 13\) (b) \(1 / 51\) (c) \(1 / 221\) (d) \(2 / 21\)

Find the probability of getting an odd number on the uppermost face in throwing a dice. [MP-88, 91, 93, 98]

Six boys and six girls sit in a row. What is the probability that the boys and girls sit alternatively? (a) \(\frac{1}{462}\) (b) \(\frac{1}{924}\) (c) \(\frac{1}{2}\) (d) None of these

One card is drawn randomly from a pack of 52 cards. Find the probability of it being an ace or a king. \([M P-2000,2004(C)]\)

What is the probability that when one die is thrown, the number appearing on top is even? (a) \(1 / 6\) (b) \(1 / 3\) (c) \(1 / 2\) (d) None of these

One ticket is drawn at random from a wellshuffled 12 ticket numbers 1 to 12 . Find the probability that the number written on the face of this ticket is a multiple of 2 or 3 . [MP-91, 94, 2000, 2001, 2008, 2009]

Five persons entered the lift cabin on the ground floor of an 8 -floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first. Find out the probability of all 5 persons leaving at different floors. (a) \(\frac{1}{7^{5}}\) (b) \(\frac{1}{{ }^{7} P_{5}}\) (c) \(\frac{{ }^{7} P_{5}}{7^{5}}\) (d) None of these

Two cards are drawn from a well-shuffled pack of cards. Find the probability that both of them are aces. [MP-95, 2000]

A bag contains 3 red, 4 white and 5 black balls. Three balls are drawn at random. The probability of being their different colours is (a) \(3 / 11\) (b) \(2 / 11\) (c) \(8 / 11\) (d) None of these

Find the probability distribution of the number of 6 in 3 throws of a dice. [MP-2009]

Three numbers are selected one by one from whole numbers 1 to 20 . The probability that they are consecutive integers is (a) \(1 / 380\) (b) \(3 / 190\) (c) \(3 / 20\) (d) None of these

A bag contains 3 red, 4 white and 5 blue balls. All balls are different. Two balls are drawn at random. Find the probability that they are of different colours. [MP-2008]

The probability that the 3 cards drawn from a pack of 52 cards are all red is (a) \(1 / 17\) (b) \(3 / 19\) (c) \(2 / 19\) (d) \(2 / 17\)

The odds against throwing 7 with 2 dice in a throw are: (a) \(5: 1\) (b) \(1: 5\) (c) \(1: 4\) (d) \(3: 1\)

For an event, odds against is \(6: 5\). The probability that event does not occur is (a) \(5 / 6\) (b) \(6 / 11\) (c) \(5 / 11\) (d) \(1 / 6\)

A die is tossed. The event an even or a prime number occurs on the top of the die is (a) \(\\{2,5\\}\) (c) \(\\{1,2,3,5\\}\) (b) \(\\{2,3,4,5,6\\}\) (d) None of these

Let \(A\) and \(B\) be two events such that \(P(A)=0.3\) and \(P(A \cup B)=0.8\). If \(A\) and \(B\) are independent events, then \(P(B)\) is (a) \(5 / 6\) (b) \(5 / 7\) (c) \(3 / 5\) (d) \(2 / 5\)

One number is selected from 1 to 100 integers. The probability that it is divisible by 6 or 8 (but not by 24 ) is (a) \(4 / 5\) (b) \(1 / 5\) (c) \(6 / 25\) (d) \(1 / 4\)

If \(A\) and \(B\) are two independent events such that \(P\left(A \cap B^{\prime}\right)=3 / 25\) and \(P\left(A^{\prime} \cap B\right)=8 / 25\), then \(P(A)\) is (a) \(1 / 5\) (c) \(2 / 5\) (b) \(3 / 8\) (d) \(4 / 5\)

Among 600 bolts, \(20 \%\) are very large \(10 \%\) are very small and the remaining are useful. One bolt is chosen at random. The probability that it is a useful bolt is (a) \(1 / 10\) (b) \(3 / 10\) (c) \(7 / 10\) (d) \(8 / 10\)

A book has 1000 pages, which are numbered from 1 to 1000 . If a page is selected at random, then the probability that the sum of the digits of its number is 9 will be (a) \(33 / 1000\) (b) \(44 / 1000\) (c) \(55 / 1000\) (d) \(66 / 1000\)

If \(A\) and \(B\) are two events such that \(P(A \cup B)+\) \(P(A \cap B)=7 / 8\) and \(P(A)=2 P(B)\), then \(P(A)\) is (a) \(7 / 12\) (b) \(7 / 24\) (c) \(5 / 12\) (d) \(17 / 24\)

One mapping is selected from all mappings which can be defined from a set \(A=\\{1,2,3\) \(\ldots, n\\}\) to \(A\). The probability that it is one-one will be: (a) \(1 / n !\) (b) \(1 / n^{n}\) (c) \(n ! / n^{n-1}\) (d) \((n-1) ! / n^{n-1}\)

Three fair coins are tossed. If both heads and tails appears, then the probability that exactly one head appears is (a) \(3 / 8\) (b) \(1 / 6\) (c) \(1 / 2\) (d) \(1 / 3\)

Two cards are drawn from a pack of 52 cards. What is the probability that one of them is a queen and the other is an ace? (a) \(2 / 663\) (b) \(2 / 13\) (c) \(4 / 663\) (d) \(8 / 663\)

A dice is rolled three times, the probability of getting a larger number than the previous number each time is (a) \(\frac{15}{216}\) (b) \(\frac{5}{54}\) (c) \(\frac{13}{216}\) (d) \(\frac{1}{18}\)

The probability of getting a number greater than 2 in throwing a die is (a) \(1 / 3\) (b) \(2 / 3\) (c) \(1 / 2\) (d) \(1 / 6\)