Equally Likely Events

Q.

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

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

2. $\frac{27}{100}$

3. $\frac{3}{10}$

4. $\frac{29}{100}$

Q.

If two different dice are rolled together, the probability of getting an even number on both dice is:

Q. Question 14.
A bag contains slips numbered from 1 to 100. If Fatima chooses a slip at random from the bag, it will either be an odd number or an even number. Since, this situatio has only two possible outcomes, so the probability of each is $\frac{1}{2}.$ Justify.

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 '4' and '5' respectively. What is the probability of getting '2' when the die is rolled? (All outcomes are equally likely).

1. $\frac{1}{2}$
2. $\frac{1}{4}$
3. $\frac{1}{3}$
4. $\frac{3}{8}$

Q. A box contains 20 tickets which are numbered from 1 to 20. If one card is drawn at random from the box, find the probability that the drawn card bears a perfect square number.

1. $\frac{1}{20}$
2. $\frac{3}{20}$
3. $\frac{1}{5}$
4. $\frac{1}{10}$

Q. A number is selected at random from the numbers from 1 to 30. Find the probability that the selected number is either even or odd.

1. 1
2. 0.75
3. 0.25
4. 0.5

Q.

What is probability?

Q.

What is sample space

Q. Question 42(i)
At a fete, cards bearing numbers 1 to 1000, one number on one card, are put in a box. Each player selects one card at random and that card is not replaced. If the selected card has a perfect square greater than 500, the player wins a prize. What is the probability that the first player wins a prize?

Q.

For three events $A,B$ and $C,$ $P$ (Exactly one of $A$or $B$occurs) $=P$(Exactly one of $B$or $C$ occurs)$=P$(Exactly one of $C$or $A$ occurs) $=\frac{1}{4}$and $P$(All the three events occur simultaneously) $=\frac{1}{16}$ Then the probability that at least one of the events occurs is

1. $\frac{7}{16}$

2. $\frac{7}{64}$

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

4. $\frac{7}{32}$

Q. A box contains 20 tickets which are numbered from 1 to 20. If one card is drawn at random from the box, find the probability that the drawn card bears a perfect square number.

1. $\frac{1}{20}$
2. $\frac{1}{10}$
3. $\frac{3}{20}$
4. $\frac{1}{5}$

Q. Which of the following events are equally likely events ?

1. Landing on one of its face when a matchbox is thrown.
2. Getting number '6' on a throw of a die.
3. Getting a 'head' on tossing of a coin.
4. Drawing a ball from a box containing balls of different colors and sizes.

Q. 5 defective glasses are accidentally mixed with 20 good ones. The good glasses and the defective ones look the same from outside. If a glass is chosen at random, what is the probability that the chosen glass is good?

1. 0.8

Q. An integer is chosen at random between 1 and 100. Find the probability that it is :
(i) divisible by 8.
(ii) not divisible by 8.

Q. A bag contains cards numbered from 2 to 90. A card is drawn at random. Find the probability that the card drawn is a perfect square.

1. $\frac{4}{31}$
2. $\frac{1}{31}$
3. $\frac{2}{45}$
4. $\frac{8}{89}$

Q. There are 3 men and 2 women. A 'Gramswachhatta Abhiyan' committee of two is to be formed:
P is the event that the committee should contain a least one woman.
Q is the event that the committee should contain one man and one woman.
R is the event that there should not be a woman in the committee.

Q. What is the probability that a leap year, selected at random will contain (i) 53 Fridays (ii) 53 Mondays and 53 Tuesdays (iii) 53 Sundays and 53 Thursdays.

Q. The table given below shows the colors of jackets in a clothing store and their respective frequencies.

Color of jacket	Frequency
Blue	$20$
Black	$30$
Brown	$50$
Grey	$100$

If a jacket is picked at random, what color do you think it would be?

1. Blue
2. Black
3. Brown
4. Grey

Q. A number is selected at random from the numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11....................... 95, 96, 97, 98, 99, 100. What is the probability that the sum of digits of the selected number is 10?

1. 0.9
2. 0.09
3. 0.1
4. 0.01

Q. 5 defective glasses are accidentally mixed with 20 good ones. The good glasses and the defective ones look the same from outside. If a glass is chosen at random, what is the probability that the chosen glass is good?

1. 0.8

Q. A dice is thrown twice. Find the probability of getting a bigger value on the first throw.

Q. 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 different days?

Q. If two coins are tossed then find the probability of the events.
(i) at least one tail turns up
(ii) no head turns up
(iii) at the most one tail turns up.

Q. 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. A number is selected at random from the numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11....................... 95, 96, 97, 98, 99, 100. What is the probability that the sum of digits of the selected number is 10?

1. 0.9
2. 0.09
3. 0.1
4. 0.01

Q.

A bag contains 6 black, 7 red and 2 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is black or white.

1. $\frac{8}{15}$

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

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

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