Introduction to Probability

Q.

There are two boxes, each containing slips numbered 1 to 5. One slip is drawn from each box and their numbers added. What are the possible sums? Compute the probability of each sum.

Q.

A single 6-sided die is rolled. What is the probability of getting a 2 or 5?

1. 1/3

2. 2/5

3. 3/5

4. 1/2

Q. A bag contains three green marbles, four blue marbles and two orange marbles. If a marble is picked at random, then the probability that it is not an orange marble is__.

1. $\frac{1}{4}$
2. $\frac{1}{3}$
3. $\frac{4}{9}$
4. $\frac{7}{9}$

Q.

Two dice, one blue and one grey, are thrown at the same time.

(i) Write down all the possible outcomes and complete the following table:

Event: Sum of two dice	2	3	4	5	6	7	8	9	10	11	12
Probability

(ii) A student argues that ‘there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability. Do you agree with this argument?

Q. Two dice, one blue and one grey, are thrown at the same time. Complete the following table:

Event: Sum on two dice	2	3	4	5	6	7	8	9	10	11	12
Probability

From the above table a student argues that there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability $\frac{1}{11}.$ Do you agree with this argument?

Q. Two different dice are tossed together. Find the probability that

(i) the number on each die is even,
(ii) the sum of the numbers appearing on the two dice is 5.

Q. Two dice are rolled. Find the number of favourable outcomes when the sum of the digits on the upper face is not less than 10.

1. 10
2. 12
3. 8
4. 6

Q. Cards each marked with one of the numbers 4, 5, 6, ..., 20 are placed in a box and mixed thoroughly. One card is drawn at random from the box. What is the probability of getting an even number?

Q.

How many outcomes does the event "Getting a sum not less than 10" when rolling two dice have?

1. 4
2. 5
3. 6
4. 8

Q.

Suppose you drop a die at random on the rectangular region shown in the given figure. What is the probability that it will land inside the circle with diameter 1 m?

Q. When two dice are tossed together, find the probability that the sum of numbers on their tops is less than 7.

Q.

Number of outcomes for the event 'getting at least one head' in the tossing of two coins is ______

1. 4
2. 3
3. 2
4. 1

Q. a dice is tossed once . find the probability of getting an even number or a multiple of 3

Q.

The data below shows the number of times of all outcomes of a dice. Find the frequency of getting a number greater than 2 but less than or equal to 5.

1. 10

2. 12

3. 22

4. 18

Q. Two dice are thrown together. The probability of getting the same number on the both dice is [CBSE 2012]

(a) $\frac{1}{2}$
(b) $\frac{1}{3}$
(c) $\frac{1}{6}$
(d) $\frac{1}{12}$

Q. A dice is rolled twice. Find the probability that

(i) 5 will not come up either time

(ii) 5 will come up exactly one time [CBSE 2014]

Q. 2 dice are thrown simultaneously , what is probability that sum of numbers appearing on dice is :a prime number , 7 & 1

Q. Two different dice are rolled simultaneously. Find the probability that the sum of the numbers on the two dice is 10.

Q. The probability that a number selected at random from the numbers 1, 2, 3, ..., 15 is a multiple of 4, is [CBSE 2014]

(a) $\frac{4}{15}$
(b) $\frac{2}{15}$
(c) $\frac{1}{5}$
(d) $\frac{1}{3}$

Q. There are 25 tickets numbered 1, 2, 3, 4, ..., 25 respectively. One ticket is draw at random. What is the probability that the number on the ticket is a multiple of 3 or 5?
(a) $\frac{2}{5}$
(b) $\frac{11}{25}$
(c) $\frac{12}{25}$
(d) $\frac{13}{25}$

Q. How many weeks are there in a leap year?

1. 53
2. 51
3. 50
4. 52

Q. Question 21
A card is drawn from a deck of 52 cards. The event E is that card is not an ace of hearts. The number of outcomes favourable to E is
(a) 4
(b) 13
(c) 48
(d) 51

Q.

Fill in the blank with a suitable option:

He said, It may rain later in the day. He said that it _________ rain later in the day

1. Would

2. May

3. Might

4. Must

Q. Probability of getting a 3 or 6 in the rolling of an unbiased die is ______

1. $\frac{1}{3}$
2. $\frac{1}{6}$
3. $\frac{2}{3}$
4. 0

Q. Cards, each marked with one of the numbers 6, 7, 8, ..., 15, are placed in a box and mixed thoroughly. One card is drawn at random from the box. What is the probability of getting a card with a number less than 10?
(a) $\frac{3}{5}$
(b) $\frac{1}{3}$
(c) $\frac{1}{2}$
(d) $\frac{2}{5}$

Q. Mark the correct alternative in each of the following:

A die is thrown once. The probability of getting a prime number is

(a) $\frac{2}{3}$ (b) $\frac{1}{3}$ (c) $\frac{1}{2}$ (d) $\frac{1}{6}$ [CBSE 2013]

Q. There are 30 cards numbered from 1 to 30. One card is drawn at random. Find the probability that the number on the selected card is not divisible by 3.

Q.

Choose whether the outcomes are impossible, unlikely, even chance, likely, or certain:

When a coin is tossed, heads will come up.

Q. Cathy rolled a pair of fair dice. What is the probability of getting a prime number as a sum of the numbers appearing on the dice?

1. $\frac{7}{12}$
2. $\frac{5}{18}$
3. $\frac{5}{12}$
4. $\frac{12}{5}$

Q.

two dice are thrown together . find the probability of that the product of the numbers on the top of the dice is (a)6 (b)12 (c( 7