Experimental Approach to Probability

Q. The probability of getting a prime number when a die is rolled is $\frac{1}{2}$.

1. False

2. True

Q.

Find the probability of getting a head when a coin is tossed once. Also find the probability of getting a tail.

1. Zero

2. 1

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

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

Q.

A multiple-choice examination has $5$questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get $4$ or more correct answers just by guessing is

1. $\frac{17}{3^5}$

2. $\frac{13}{3^5}$

3. $\frac{11}{3^5}$

4. $\frac{10}{3^5}$

Q. Two dice are rolled simultaneously. The probability that they show different faces is:

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

Q.

Six coins are tossed simultaneously the probability of getting at least $4$ heads is___________.

Q.

A die is rolled three times. The probability of getting a larger number than the previous number each time is

1. $\frac{5}{72}$

2. $\frac{5}{54}$

3. $\frac{13}{16}$

4. $\frac{1}{18}$

Q.

A coin is tossed 60 times and the tail appears 35 times. What is the probability of getting a head?

1. $\frac{12}{7}$

2. $\frac{7}{12}$

3. $\frac{5}{12}$

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

Q.

From a set of 17 cards, numbered 1, 2, ..., 17, one is drawn. What is the probability that the number is multiple of 3 or 7?

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

2. $\frac{6}{17}$

3. $\frac{7}{17}$

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

Q.

A ball is picked from a bag containing blue balls and red balls, and then replaced into the bag. This experiment is performed 50 times. The result was 15 blue and 35 red. Find the probability of drawing (i) a blue ball (ii) a red ball. [2 MARKS]

Q.

A book has pages numbered from 1 to 85. What is the probability that the sum of the digits on the page is 8 if a page is chosen at random?

1. 6/85

2. 7/85

3. 9/85

4. 8/85

Q.

Three coins are tossed at once. What is the probability of two heads and one tail?

Q.

A letter is chosen from the word 'PROBABILITY'. What is the probability that the letter chosen is a consonant?

1. $\frac{5}{11}$

2. $\frac{4}{11}$

3. $\frac{9}{11}$

4. $\frac{7}{11}$

Q.

There are 5 green, 6 black and 7 white balls in a bag. A ball is drawn at random from the bag. Find the probability that it is not white.

1. 11/18

2. 2/3

3. 5/18

4. 7/18

Q.

A bag contains 8 red, 2 black and 7 white balls. One ball is drawn at random. The probability that the ball drawn is not white is

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

2. $\frac{10}{17}$

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

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

Q.

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 die is dropped at random on the rectangular region of sides $3m\times 2m$. What is the probability that it will land inside a circle(lying inside the rectangle) with diameter 1 m?

1. $\frac{\pi }{48}$
2. $\frac{\pi }{24}$
3. $\frac{\pi }{36}$
4. $\frac{\pi }{12}$

Q.

A die is rolled 100 times and the outcomes are recorded as below. What is the probability of getting

(i) an odd number ?
(ii) an even number ?

$\begin{array}{ccccc}Outcome& 1& Evennumber<6& Oddnumber>1& 6\\ Frequency& 15& 33& 36& 16\end{array}$

[2 MARKS]

Q.

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

1. 
2. 
3. 
4. 

Q.

A letter is chosen from the word 'GEOMETRY'. What is the probability that the letter chosen is a vowel?

1. $\frac{5}{8}$

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

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

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

Q.

On tossing three coins simultaneously, find the probability of getting at least one head and tail.

1. 1/4

2. 1/2

3. 3/4

4. 2/3

Q.

Question 27
In a medical examination of students of a class, the following blood groups are recorded.

$\begin{array}{ccccc}\text{Blood group}& A& AB& B& O\\ \text{Number of}& 10& 13& 12& 5\\ \text{students}& & & & \end{array}$

A student is selected at random from the class. The probability that he/she has blood group B is:

A) $\frac{1}{4}$
B) $\frac{13}{40}$
C) $\frac{3}{10}$
D) $\frac{1}{8}$

Q.

Three fair coins are tossed. If both heads and tails appear, then the probability that exactly one head appears is

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

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

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

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

Q.

Out of 50 students in a class taking a test, 35 of them passed whereas the other 15 failed. The probability that a student selected at random passed the exam is 0.8.

1. 0.15

2. 0.3

Q.

A bag contains 6 white and 3 black balls. When a ball is drawn without looking, the probability that the ball is black is ___.

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

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

3. $0$

4. $1$

Q. Question 15 (ii)
Five cards – ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random. If the queen is drawn and put aside, what is the probability that the second card picked up is (a) an ace? (b) a queen?

Q.

A die is thrown 500 times and the outcomes 1, 2, 3, 4, 5, 6 have frequencies as given below

$$\begin{array}{ccccccc}\text{Outcome}& 1& 2& 3& 4& 5& 6\\ \text{Frequency}& 75& 85& 90& 80& 75& 95\end{array}$$

What is the probability of getting a value greater than or equal to 4?

1. 2

2. 0.5

3. 0.34

4. 0.68

Q.

The probability of getting a composite number in a throw of dice is ___.

1. 1/2

2. 1

3. 1/3

4. 1/6

Q.

One Card is drawn from a deck of$52$. What is the probability that it is a diamond?

Q.

From the word 'CHOCOLATE', a letter is selected at random. The probability that the chosen letter is a vowel is ___.

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

2. $\frac{5}{9}$

3. $\frac{4}{9}$

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

Q.

A bag contains coins numbered from 1 to 50. If one coin is picked up at random, find the probability that it bears a square number.

1. $\frac{7}{50}$

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

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

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