Probability of an Event

Q. A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability of getting neither a red card nor a queen.

Q. There are 100 cards in a bag on which numbers from 1 to 100 are written. A card is taken out from the bag at random. Find the probability that the number on the selected card (i) is divisible by 9 and is a perfect square, (ii) is a prime number greater than 80.

Q.

How many aces are present in a deck of cards?

1. 13

2. 4

3. 26

4. 3

Q.

Each of the faces of a fair six-sided number cube is numbered with one of the numbers $1$ through $6$, with a different number appearing on each face.

Two such number cubes will be tossed, and the sum of the numbers appearing on the faces that land up will be recorded.

What is the probability that the sum will be $4$, given that the sum is less than or equal to $6$ ?

Q.

Find the probability of getting at least two heads if three coins are tossed simultaneously.

1. $\frac{1}{8}$

2. $\frac{3}{8}$

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

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

Q.

A coin is tossed thrice. What is the probability of getting a Head in the second toss and a Tail in the third? [2 MARKS]

Q.

Three squares of a chess board are chosen at random, the probability that two are of one color and one of another is

1. $\frac{16}{21}$

2. $\frac{8}{21}$

3. $\frac{32}{12}$

4. None of these

Q.

A box contains 19 balls bearing numbers 1, 2, 3…… 19. A ball is drawn at random from the box. What is the probability that the number on the ball is

a) a prime number

b) divisible by 3 or 5

Q.

Two cards are drawn at random from a pack of $52$ cards. The probability of getting at least a spade and an ace is:

Q. What is the probability of not getting a prime number when a die is rolled?

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

Q.

A bag $x$ contains $3$ white balls and $2$ black balls and another bag $y$ contains $2$ white balls and $4$ black balls. A bag and a ball out of it are picked at random. The probability that the ball is white is

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

2. $\frac{7}{15}$

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

4. None of these

Q.

A single die is rolled. The probability of getting 1 or an even number is

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

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

3. $\frac{4}{6}$
4. $\frac{5}{6}$

Q.

In a lottery of $50$ tickets numbered $1$ to $50$, two tickets are drawn simultaneously. The probability that both the tickets are drawn have prime numbers is ?

Q.

What is the sum of the probabilities of getting a head and getting a tail when a coin is tossed once?

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

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

3. 1

4. 0

Q. Find the probability of getting an even number on the die and tail on the coin, if a die and a coin both are tossed simultaneously.

1. 
   $\frac{1}{12}$
2. 
   $\frac{1}{3}$
3. 
   $\frac{1}{4}$
4. 
   $\frac{1}{6}$

Q. In the famous bollywood movie Sholay, Jai uses a coin in which both the faces are same i.e., heads. Jai always uses this coin to settle disputes with his friend named Viru by tossing it. In the case of a toss, Jai always calls heads. What is the probability that Jai will win the toss?

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

Q. If two dice are thrown, what is the probability that the sum is neither 9 nor 12 ?

1. 
   $\frac{31}{36}$
2. 
   $\frac{8}{9}$
3. 
   $\frac{11}{12}$
4. 
   $\frac{5}{6}$

Q.

There is a box containing 10 ping pong balls of 3 different colours red, green and blue. There are 2 red balls and 3 green balls. What is the probability of getting a blue ball in the first attempt?

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

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

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

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

Q. Question 22 (i)
(i) Complete the following table:
$\begin{array}{cccccccccccc}\text{Event: Sum of 2 dice}& 2& 3& 4& 5& 6& 7& 8& 9& 10& 11& 12\\ \text{Probability}& \frac{1}{36}& & & & & & \frac{5}{36}& & & & \frac{1}{36}\end{array}$

Q.

A box contains $9$ tickets numbered $1$ to $9$ inclusive. If $3$ tickets are drawn from the box without replacement, the probability that they are alternatively either {odd, even odd} or {even, odd, even} is

1. $\frac{5}{17}$

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

3. $\frac{5}{16}$

4. $\frac{5}{18}$

Q.

Two dice are thrown simultaneously. Find the probability that:

i) both the dice show the same number

ii) the first die shows 6

iii) the total (sum) of the numbers on the dice is 9.

1. 

2. 

3. 

4. 

5. 

6. 

7. 

Q.

Define elementary event and compound event.

Q.

A bucket contains 10 brown balls, 8 green balls, and 12 red balls and you pick one randomly without looking. What is the probability that the ball will be brown?

1. $\frac{4}{15}$

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

3. 0.61

4. 0.33

Q. Question 14 (v)
One card is drawn from a well–shuffled deck of 52 cards. Find the probability of getting a spade.

Q. Question 14 (ii)
One card is drawn from a well–shuffled deck of 52 cards. Find the probability of getting a face card.

Q. Which of the following events are not equally likely events?

1. Getting number '6' on a throw of a die.
2. Drawing a ball from a box containing balls of different colors and sizes.
3. Getting tail on a toss of a coin.
4. Drawing a ball from a box containing balls of different colors same sizes.

Q. Question 11
Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fishes and 8 female fishes (see figure). What is the probability that the fish taken out is a male fish?

Q. Question 14 (vi)
One card is drawn from a well–shuffled deck of 52 cards. Find the probability of getting the queen of diamonds.

Q. Question 20(iii)
Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is 1?

Q.

When a die was rolled 60 times, the following was observed.

$\begin{array}{ccccccc}\text{Outcome}& 1& 2& 3& 4& 5& 6\\ \text{Frequency}& 9& 10& 12& 13& 7& 9\end{array}$

(i) Which number had an experimental probability that matched the theoretical probability?

(ii) How many numbers had an experimental probability that was less than that which would have been predicted by theoretical probability?