Theoretical Probability

Q.

A card is drawn from a pack of 52 cards. The probability of getting an ace is $\frac{1}{52}$.

1. True

2. False

Q.

The probability of getting a face card from a well-shuffled pack of 52 cards is___

1. 3/13
2. 1/13
3. 1/52
4. 4/13

Q.

The probability of getting a sum of 5 on rolling two dice is $\frac{1}{11}$.

1. True

2. False

Q. What is the probability that a leap year has 53 Sundays and 53 Mondays?

1. $\frac{4}{7}$
2. $\frac{3}{7}$
3. $\frac{1}{7}$
4. $\frac{2}{7}$

Q.

The probability of drawing a black face card from a deck of 52 is $\frac{1}{2}$.

1. True

2. False

Q.

Two unbiased dice are thrown. Find the probability that the total of the numbers on the dice is greater than 10.

Q. Two customers are visiting a particular shop in the same week (Monday to Saturday). Each is equally likely to visit the shop on any one day as on another. What is the probability that both will visit the shop on:

(i) the same day?

(ii) Different days?

(iii) consecutive days?

Q. A number is selected from first 50 natural numbers. What is the probability that it is a multiple of 3 or 5?

(a) $\frac{13}{25}$

(b) $\frac{21}{50}$

(c) $\frac{12}{25}$

(d) $\frac{23}{50}$

Q.

Cards marked with numbers 5 to 50 are placed in a box and mixed thoroughly. A card is drawn from the box at random. Find the probability that the number on the taken out card is (i) a prime number less than 10 (ii) a number which is a perfect square.

Q.

When a card is drawn from a pack of 52 cards. The probability that it may be either a king or a queen is $\frac{2}{13}$.

1. False

2. True

Q.

From a pack of $52$ cards, two cards are drawn one by one without replacement. The probability that first drawn card is a king and second is a queen, is

1. $\frac{2}{13}$

2. $\frac{8}{663}$

3. $\frac{4}{663}$

4. $\frac{103}{663}$

Q.

In class 10 A , there are 24 boys and 25 girls. In class 10B , there are 20 boys and 20 girls. One student is selected from each class for an activity. What is the probability of both of them being girls ?

1. $\frac{25}{98}$

2. $\frac{24}{95}$

3. $\frac{15}{23}$

4. $\frac{21}{50}$

Q.

Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. A box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was drawn from Box I is:

1. $\frac{4}{17}$

2. $\frac{8}{17}$

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

4. $\frac{2}{3}$

Q.

A bag contains $19$ tickets numbered from $1$ to $19$. A ticket is drawn and then another ticket is drawn without replacement. The probability that both the tickets will show even number is

1. $\frac{9}{19}$

2. $\frac{8}{18}$

3. $\frac{9}{18}$

4. $\frac{4}{19}$

Q.

A die thrown. Find the probability of getting :

(i) a prime number

(ii) 2 or 4

(iii) a multiple of 2 or 3

(iv) an even prime number

(v) a number greater than 5

(vi) a number lying between 2 and 6

Q.

A box 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 drawn card is (i) divisible by 2 or 3, (ii) prime number.

Q. If a two digit number is chosen at random, then the probability that the number chosen is a multiple of 3, is

(a) $\frac{3}{10}$

(b) $\frac{29}{100}$

(c) $\frac{1}{3}$

(d) $\frac{7}{25}$

Q.

A card is drawn at random from a pack of $52$ cards. The probability that the drawn card is a court card i.e., a jack, queen or a king is

1. $\frac{3}{52}$

2. $\frac{3}{13}$

3. $\frac{4}{13}$

4. None of these

Q.

A number is chosen at random among the first 100 natural numbers. Find the probability that the number chosen is prime.

1. 1/4

2. 27/100

3. 3/10

4. 29/100

Q. Question 23
A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result, i.e., three heads or three tails and loses otherwise. Calculate the probability that Hanif will lose the game.

Q.

A card is drawn from a well shuffled deck of 52 cards. What is the probability of getting a spade?

1. 1/8

2. 1/6

3. 1/4

4. 1/10

Q. A bag contains 5 red, 8 green and 7 white balls, One ball is drawn at random from the bag. What is the probability of getting a white ball or a green ball?

Q.

The probability of selecting a green marble at random from a jar that contains only green, white and yellow marbles is $\frac{1}{4}$. The probability of selecting a white marble at random from the same jar is $\frac{1}{3}$.1f this jar contains 10 yellow marbles, what is the total number of marbles in the jar?

Q.

Cards bearing numbers 3 to 20 are placed in a bag and mixed thoroughly. A card is taken out randomly from the bag. What is the probability that the number on the card is an even number?

1. $\frac{2}{3}$

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

3. $1$

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

Q.

In a lottery there are 10 prizes and 25 blanks. What is the probability of getting a prize?

Q.

All red face cards are removed from a pack of playing cards. The remaining cards are well shuffled and then a card is drawn at random from them. Find the probability that the drawn card is: (i) a red card (ii) a face card and (iii) a card of clubs.

Q. Question 40(i)
A lot consists of 48 mobile phones of which 42 are good, 3 have only minor defects, 3 have major defects. Varnika will buy a phone if it is good but the trader will only buy a mobile if it has no major defect. One phone is selected at random from the lot. What is the probability that it is acceptable to Varnika?

Q.

Two dice are thrown. What is the probability that the sum of the numbers appearing on the two dice is $11,$ if $5$ appears on the first $?$

1. $\frac{1}{36}$

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

3. $\frac{5}{6}$

4. None of these

Q.

What is meant by a doublet in probability. With examples.

Q. Question 08.
When we toss a coin, there are two possible outcomes - head or tail. Therefore, the probability of each outcome is $\frac{1}{2}.$ Justify your answer.