Probability Test

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Probability Test - 6

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Weekly Quiz Competition

Question 1
1 / -0

There are 36 cards, numbered 1 to 36. One card is drawn at random. What is the probability that the number on this card is not divisible by 5?

A

B

C

D

Solution

Total number of cards = 36

Numbers divisible by 5 from 1 to 36: 5, 10, 15, 20, 25, 30 and 35

Number of cards containing numbers divisible by 5 = 7

Number of cards containing numbers not divisible by 5 = 36 - 7 = 29

Required probability =
Question 2
1 / -0

A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of drawing a 2 of spades or a 9 of spades.

A

B

C

D

Solution

Total number of cards in the deck = 52
Number of favourable cases (a 2 of spades or a 9 of spades) = 2
Required probability =
Question 3
1 / -0

If a fair coin is tossed twice, what is the probability of getting heads in both the trials?

A

B

C

D
1

Solution

Probability of getting a head in a single toss of coin =
Probability of getting head when the coin is tossed twice = =
Question 4
1 / -0

From a deck of 52 cards, find the probability of selecting a card containing a multiple of 3 or 7.

A

B

C

D

Solution

Total number of cards with multiples of 3 = 12 (3, 6 and 9 of each suit)
Total number of cards having multiples of 7 = 4 (1 of each suit)

Required probability =
=

=
Question 5
1 / -0

Tickets numbered from 1 to 25 are mixed up together and a ticket is drawn at random. What is the probability that the ticket drawn has a prime number?

A

B

C

D

Solution

Favourable cases = 2, 3, 5, 7, 11, 13, 17, 19, 23 = 9
Hence, probability =
Question 6
1 / -0

A card is drawn at random from a deck of 52 cards. Find the probability of getting a red king or a black jack.

A

B

C

D

Solution

Number of red kings = 2
Number of black jacks = 2

Required probability =
=

=
Question 7
1 / -0

A pair of dice is thrown and the numbers appearing have a sum greater than or equal to 10. The probability of getting a sum of 11 is

A

B

C

D

Solution

Total number of possible cases = (4, 6) (5, 5) (6, 4) (6, 6) (5, 6) (6, 5) = 6
Favourable events = (5, 6) or (6, 5) = 2
Required probability = =
Question 8
1 / -0

The probability of having 53 Mondays in a non-leap year is

A

B

C

D

Solution

A non-leap year has 365 days, i.e. 52 weeks and 1 day.
Now, for 53 Mondays, the extra/odd day has to be a Monday.
Now, the probability of extra day being a Monday = .

Question 9

1 / -0

Directions: Study the given data and answer the following question:

The table below gives the points scored by different students in a game:

Points (Class Interval)	1-10	11-20	21-30	31-40	41-50
Number of students (Frequency)	15	20	10	25	5

Out of all these students, one student is chosen at random. What is the probability that the points scored by the chosen student are 21 or more?

Solution

Total number of students = 15 + 20 + 10 + 25 + 5 = 75
Number of students who scored 21 points or more = 10 + 25 + 5 = 40

Required probability = =

Question 10

1 / -0

Rahul, a Mathematics teacher, conducts an activity in a class. The activity involves tossing 3 coins simultaneously 150 times with the following frequencies of different outcomes:

Outcomes	3 heads	2 heads	1 head	No head
Frequency	65	43	19	23

Find the probability of getting less than 2 heads in the given activity.

Solution

Total number of outcomes = 150
Number of favourable outcomes = 19 + 23 = 42
Required probability ===

Question 11
1 / -0

Two dice, A and B, are rolled at the same time. The sum of the two numbers obtained is 7. What is the probability that the number obtained on die A is greater than that obtained on die B.

A

B

C

D

Solution

Let the event of getting a bigger number on A than on B be Q.
There are six ways to get a sum of 7 when two dice are rolled = (A, B) = {(2, 5), (1, 6), (3, 4), (5, 2),(4, 3), (6,1)}
Among these, there are three cases in which the number on A is greater than that on B: {(5, 2), (6, 1), (4, 3)}
Q = {(5, 2), (6, 1), (4, 3)}
Therefore, number of favourable case = 3
Total number of ways of getting a sum of 7 = 6

Required probability = 3/6 =
Question 12
1 / -0

The probability of finding the correct match to a question is . If the probability of not finding the correct match is , then find the value of x.

A
21

B
18

C
12

D
9

Solution

P (Correct) =

P (Not correct) =

So, P (Not correct) = 1 - P (Correct)

= 1 –

x = 18
Question 13
1 / -0

What is the probability that the given spinner will stop either on a composite number or on a prime number?

A
0

B

C

D
Cannot be determined

Solution

1 is neither prime nor composite.
2, 3 and 5 are prime numbers.
4 is a composite number.
Total possible outcomes = 13
Total favourable outcomes = 13 - 3 = 10
P(prime or composite number) = =
Question 14
1 / -0

In a pack of cards numbered from 1 to 100, how many favourable outcomes are there for picking a card containing a number that is divisible by 5?

A
19

B
10

C
20

D
9

Solution

Let A be the event of picking a card containing a number divisible by 5.
So, A = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100}
Therefore, number of favourable outcomes = 20
Question 15
1 / -0

There are 6 blue, 5 red, 3 orange and 2 yellow balls in a box. A ball is drawn at random from the box. What is the probability that the ball selected is not orange?

A

B

C

D

Solution

Total number of balls = 6 + 5 + 3 + 2 = 16
Number of orange balls = 3
Therefore, number of balls which are not orange = 16 - 3 = 13
Required probability =
Question 16
1 / -0

In a sample study of 632 students, it was observed that 518 have a degree. If a student is selected at random, then find the probability that he/she does not have a degree.

A

B

C

D

Solution

Total number of students = 632

Number of students who have a degree = 518

Number of students who do not have a degree = 632 - 518 = 114

So, required probability = =
Question 17
1 / -0

A bag contains 3 orange, 2 yellow and 5 white balls. A ball is taken out of the bag at random. Find the probability that the selected ball is

(i) white
(ii) not yellow

A
(i), (ii)

B
(i), (ii)

C
(i), (ii)

D
(i), (ii)

Solution

(i) Number of favourable outcomes = 5 (Total number of white balls = 5)

Total number of possible outcomes = 10

Probability =
=

=

(ii) Number of yellow balls = 2
Number of balls that are not yellow = 10 - 2 = 8
Number of favourable outcomes = 8
Total number of possible outcomes = 10

Probability =

=

=
Question 18
1 / -0

Joseph and John are playing a card game in which a card is drawn at random from a well-shuffled deck of 52 cards by one of them. Find the probability that the card drawn is neither a spade nor a jack.

A

B

C

D

Solution

In a full deck:
Number of spade cards = 13
Number of non-spade cards = 52 - 13 = 39
Now:
Total number of jacks = 4
However, the jack of spades has already been eliminated from the deck along with other spade cards.
Number of jacks left = 1 from each of the three remaining suits = 3
So:
Number of cards that are neither a spade nor a jack = 39 - 3 = 36

Therefore, required probability = =
Question 19
1 / -0

An anti-aircraft gun can fire only 4 shots at an enemy plane. The probabilities of hitting the plane in the first, second, third and fourth shots are 0.4, 0.3, 0.2 and 0.1, respectively. What is the probability that the plane gets hit?

A
0.698

B
0.424

C
0.302

D
None of these

Solution

Probability that the plane gets hit
= 1 − Probability of not hitting the plane
= 1 - (1 - 0.4)(1 - 0.3)(1 - 0.2)(1 - 0.1)
= 1 - (0.6)(0.7)(0.8)(0.9)
= 1 - 0.3024
= 0.6976 0.698
Question 20
1 / -0

A box contains 14 purple marbles, 9 grey marbles and 11 blue marbles. A marble is drawn at random. What is the probability that the drawn marble is not purple?

A

B

C

D

Solution

Total number of marbles = 34
Number of marbles that are not purple = 34 - 14 = 20

Required probability =

Question 21

1 / -0

The following table gives the result of a survey asking 100 employees in a company for their favourite colour:

Choice of Colour	Frequency
Blue	20
Brown	6
Green	18
Orange	9
Purple	11
Red	28
Yellow	8
Total	100

An employee is selected at random from the group. In this context, which of the following statements is correct?

The probability of selecting an employee whose favourite colour is brown is.

The probability of selecting an employee whose favourite colour is red is.

The probability of selecting an employee whose favourite colour is yellow is.

The probability of selecting an employee whose favourite colour is purple is.

Solution

Number of employees who have yellow as their favourite colour = 8
Total number of employees = 100

Required probability ==

Question 22
1 / -0

Three friends, i.e. Joseph, John and Jack, are playing a game in which a die is rolled once.

Find:
(A) Probability of getting a prime number
(B) Probability of getting a number less than 5
(C) Probability of getting a multiple of 2

A
(A), (B), (C)

B
(A), (B), (C)

C
(A), (B), (C)

D
(A) , (B) , (C)

Solution

When a die is rolled, number of total possible outcomes = 6
(A) Prime number on a die: 2, 3, 5
Number of favourable outcomes = 3
Required probability =
(B) Numbers less than 5 on a die: (1, 2, 3, 4)
Number of favourable outcomes = 4
Required probability =
(C) Multiples of 2 on a die: 2, 4, 6
Number of favourable outcomes = 3
Required probability =
Question 23
1 / -0

Determine whether the statements are true (T) or false (F) and choose the correct alternative:

(A) Probability of an impossible event is always 1.
(B) Probability of event M = 1 + Probability of complement of event M
(C)is the probability of getting a prime number out of 1-10.
(D) When two dice and one coin are thrown simultaneously, the total number of outcomes in the sample space is 72.

A

B

C

D

Solution

(A) False
Probability of a possible event is always 1 and the probability of an impossible event is 0, which means it can never happen.

(B) False
Probability of event M = 1 - Probability of complement of event M

(C) True
Number of favourable outcomes = 4 (2, 3, 5, 7)
Probability of getting a prime number out of 1-10 =
(D) True
Total number of possible outcomes for each throw of a die is 6, and that for each toss of a coin is 2.
Therefore, total number of combined possible outcomes = 6 × 6 × 2 = 72
Question 24
1 / -0

Two dice are thrown. Find the probability that the product of two numbers received is even.

A

B

C
1

D

Solution
Question 25
1 / -0

A coin is tossed thrice.
Statement I: Probability of getting heads at least twice is .
Statement II: Probability of getting heads only once is .

Which of the two statements is/are correct?

A
Both statements I and II

B
Only statement I

C
Only statement II

D
Neither statement I nor statement II

Solution

The sample space for three fair coin flips: {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Total number of possible outcomes = 8

(I) Number of favourable outcomes (Getting heads at least twice) = 4 (HHH, HHT, HTH, THH)

Required Probability = =

(II) Number of favourable outcomes (Getting heads only once) = 3

Required Probability =

Hence, only statement I is correct.