Event and Outcomes

Q.

What are the number of possible outcomes of tossing a coin once?

1. 5

2. 4

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.

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.

Three unbiased coins are tossed together, then which of the following is true?

1. The probability of getting exactly 2 heads is $\frac{1}{2}$

2. The probability of getting atleast one head is $\frac{5}{8}$

3. The probability of getting at least 2 tails is $\frac{3}{8}$

4. The probability of getting exactly one tail is $\frac{3}{8}$

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.

There are 2 men X and Y who were born in the same year. If X's date of birth is on ${19}^{th}$December 1990, how many dates are possible for Y to be born such that he doesn't have the same birthday as X?

1. 364

2. 360

3. 365

4. 300

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.

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.

There are 21 girls and 33 boys in a classroom. I want to randomly select one student to become the class leader. If I want to find the probability that the selected student is a girl, the number of favourable outcomes is ___.

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