Event and Outcomes

Q. If two dice are rolled simultaneously, find the probability of the following events.
(1) The sum of the digits on the upper faces is at least 10.
(2) The sum of the digits on the upper faces is 33.
(3) The digit on the first die is greater than the digit on second die.

Q. A box contains cards numbered from 1 to 20. A card is drawn at random. Find the probability that the card drawn bears:
i) a prime number
ii) an even number
iii) a number divisible by 4
iv) a factor of 20
[4 MARKS]

Q. Someone is asked to take a number from 1 to 100. The probability that the selected number is prime is:

1. $\frac{1}{5}$
2. $\frac{25}{100}$
3. $\frac{1}{4}$
4. $\frac{13}{50}$

Q. Two dice are rolled together. Find the probability of getting such numbers on the two dice whose product is 12.

Q. In a simultaneous throw of pair of dice, find the probability of getting:

(i) 8 as the sum

(ii) a doublet

(iii) a doublet of prime numbers

(iv) a doublet of odd numbers

(v) a sum greater than 9

(vi) an even number on first

(vii) an even number on one and a multiple of 3 on the other

(viii) neither 9 nor 11 as the sum of the numbers on the faces

(ix) a sum less than 6

(x) a sum less than 7

(xi) a sum more than 7

(xii) at least once

(xiii) a number other than 5 on any dice.

(xiv) even number on each die [CBSE 2014, 2015]

(xv) 5 as the sum [CBSE 2014, 2015]

(xvi) 2 will come up at least once [CBSE 2015]

(xvii) 2 will not come either time [CBSE 2015]

Q. Question 06.
A game consists of spinning an arrow which comes to rest pointing at one of the regions (1, 2 or 3)(see figure). Are the outcomes 1, 2 and 3 equally likely to occur ? Give reasons.

Q. Three coins are tossed together. Find the probability of getting:

(a) exactly two heads

(b) at most two heads

(c) at least one head and one tail.

(d) no tails

Q. Two coins are tossed simultaneously. Find the probability of getting
(i) exactly 1 head
(ii) at most 1 head
(iii) at least 1 head

Q. Harpreet tosses two different coins simultaneously (say, one is of Re 1 and other of Rs 2). What is the probability that he gets at least one head?

Q. Two coins are tossed simultaneously. What is the probability of getting at least one head?

Q. 24 cards numbered 1, 2, 3, ...., 23, 24 are put in a box and mixed thoroughly. One person draws a card from the box. Find the probability that the number on the card is divisible by 2 or 3 or both.

Q. A die is thrown thrice , if the first throw is $5$, then the chance of getting $15$ as the sum is

1. $\frac{1}{12}$
2. $\frac{1}{9}$
3. $\frac{1}{108}$
4. $\frac{1}{18}$

Q. If three coins are tossed simultaneously, then the probability of getting at least two heads, is

(a) $\frac{1}{4}$

(b) $\frac{3}{8}$

(c) $\frac{1}{2}$

(d) $\frac{1}{4}$

Q. Question 1 (i)
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 the same day?

Q.

There is a pack of 52 cards. Ram removes the queen of hearts and the jack of spades from this pack. Ram now picks a card at random from this reduced pack. What is the probability that Ram picks is a Jack card?

1. 0.05

2. 0.06

3. 0.03

4. 0.07

Q.

There is a pack of 52 cards. Ram removes the queen of hearts and the jack of spades from this pack. Ram now picks a card at random from this reduced pack. What is the probability that Ram picks is a Jack card?

1. 0.05

2. 0.06

3. 0.03

4. 0.07

Q.

You have an eight-faced die. In this die, one of the faces contains 1, two faces contain 2, three faces contain 3 and other faces contain a 4 and a 5 respectively. What is the number of favourable outcomes of obtaining a 3, while a dice is thrown?

1. 4

2. 1

3. 2

4. 3

Q.

Assertion : In rolling a die, event A = {1, 3, 5} and event B = {2, 4} are mutually exclusive events.
Reason : In a sample space two events are mutually exclusive if they do not occur at the same time.

1. Both assertion and reason are true and reason is the correct explanation of assertion.

2. Both assertion and reason are true but reason is not the correct explanation of assertion.

3. Assertion is true but reason is false.

4. Assertion is false but reason is true.

Q. Question 24
One ticket is drawn at random from a bag containing tickets numberd 1 to 40. The probability that the selected ticket has a number which is a multiple of 5 is
(a) $\frac{1}{5}$
(b) $\frac{3}{5}$
(c) $\frac{4}{5}$
(d) $\frac{1}{3}$

Q.

From a pack of 52 cards, all the multiples of 3 are removed. A card is now drawn at random. What is the probability that it is a

(i) a face card ( King , Queen , Jack)

(ii) an even number red card

1. 0.3 , 0.5

2. 0.4 , 0.5

3. 0.3 , 0.25

4. 0.5 , 0.4

Q.

Which of the following numbers can never be an outcome for the single roll of an unbiased die?

1. 6

2. 7

3. 1

4. 4

Q.

Cards marked with numbers 40 , 41 , 42..........60 are well shuffled and a card is drawn at random. What is the probability that the number of the cards is

(i) a prime number

(ii) divisible by 3

(iii) a perfect square

1. (i) $\frac{1}{5}$ (ii) $\frac{3}{20}$ (iii) $\frac{1}{10}$

2. (i) $\frac{3}{4}$ (ii) $\frac{9}{20}$ (iii) $\frac{1}{10}$

3. (i) $\frac{1}{2}$ (ii) $\frac{11}{20}$ (iii) $\frac{3}{20}$

4. (i) $\frac{1}{4}$ (ii) $\frac{7}{20}$ (iii) $\frac{1}{20}$

Q.

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is black or king.

1. $\frac{1}{2}$
2. $\frac{7}{13}$
3. $\frac{15}{26}$
4. $\frac{8}{13}$

Q. A card is drawn at random from a well shuffled deck of 52 cards. Find the probability of getting a card bearing a number greater than 2 but less than 9.

1. $\frac{1}{13}$
2. $\frac{6}{13}$
3. $\frac{4}{13}$
4. $\frac{5}{13}$

Q. A piggy bank contains hundred 50 paise coins, fifity ₹1 coins, twenty ₹2 coins and ten ₹5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, find the probability that the coin which fell

(i) will be a 50 paise coin
(ii) will be of value more than ₹1
(iii) will be of value less than ₹5
(iv) will be a ₹1 or ₹2 coin [CBSE 2014]

Q. A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability?

(i) that the sum of the two numbers that turn up is 7?

(ii) of obtaining a total of 6?

(iii) of obtaining a total of 10?

(iv) of obtaining the same number on both dice?

(v) of obtaining a total more than 9?

(vi) that the sum of the two numbers appearing on the top of the dice is 13?

(vii) that the sum of the numbers appearing on the top of the dice is less than or equal to 12?

(viii) that the product of numbers appearing on the top of the dice is less than 9. [CBSE 2014]

(ix) that the difference of the numbers appearing on the top of two dice is 2. [CBSE 2014]

Q. Three coins are tossed simultaneously. What is the probability of getting at least two heads?

Q. Two dice are thrown. Find the probability of the events.

(ii) The sum of the numbers on their upper faces is multiple of 7.

Q. A random variable $X$ has the probability distribution:

$x$	1	2	3	4	5	6	7	8
$P(X=x)$	0.15	0.23	0.12	0.10	0.20	0.08	0.07	0.05

For the events $E=\left\{x|x\text{is prime}\right\}$ and $F=\{x|x<4\}$, the probability $P(E\cup F)$ is

1. $0.77$
2. $0.87$
3. $0.35$
4. $0.50$

Q.

The lock of a suitcase is 3 digit number. The owner of the suitcase has forgotten the digit at unit's place. If the digit is an even number, then the number of favorable outcomes for units place are:

1. 2

2. 4

3. 5

4. 10