Important Questions: Probability for Class 10 - Free MCQ Test with solutions

Important Questions: Probability - Question 1

If an event cannot occur, then its probability is

A.
1
B.
3/4
C.
1/2
D.
0

Detailed Solution: Question 1

The probability of an impossible event is 0 because such an event cannot occur under any circumstances.

Important Questions: Probability - Question 2

Which of the following cannot be the probability of an event?

A.
1.5
B.
3/5
C.
25%
D.
0.3

Detailed Solution: Question 2

∵ Probability of any event cannot be more than 1.
∴ 1.5 can not be the probability of any event.
∴ (a) is the answer.

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Important Questions: Probability - Question 3

An event is very unlikely to happen. Its probability is closest to

A.
0.0001
B.
0.001
C.
0.01
D.
0.1

Detailed Solution: Question 3

To determine which probability is closest to an event that's very unlikely, we compare the given options. The smallest probability provided is 0.0001, making it the correct choice as it is nearest to zero and thus represents a very low likelihood.

Important Questions: Probability - Question 4

A coin is tossed twice. The probability of getting both heads is

A.
1/2
B.
1/3
C.
1/4
D.
1

Detailed Solution: Question 4

Sample space - {HH, HT, TH, TT}
Number of total possible outcomes = 4
Number of favourable outcome (both heads) = 1
∴ Probability of getting both head = 1/4

Important Questions: Probability - Question 5

The probability expressed as a percentage of a particular occurrence can never be

A.
Less than 100%
B.
Greater than 100%
C.
Greater than 0%
D.
Anything but a whole number

Detailed Solution: Question 5

Probabilities range from 0% to 100%. Therefore, a probability expressed as a percentage can never be less than 0% or greater than 100%. Thus, option B (greater than 100%) is impossible.

Important Questions: Probability - Question 6

The probability that a non leap year selected at random will contain 53 Sunday's is

A.
1/7
B.
2/7
C.
3/7
D.
5/7

Detailed Solution: Question 6

A non-leap year has 365 days

A year has 52 weeks. Hence there will be 52 Sundays for sure.

52 weeks = 52 x 7 = 364 days .

365– 364 = 1 day extra.

In a non-leap year there will be 52 Sundays and 1day will be left.

This 1 day can be Sunday, Monday, Tuesday, Wednesday, Thursday, friday, Saturday, Sunday.

Of these total 7 outcomes, the favourable outcomes are 1.

Hence the probability of getting 53 sundays = 1/7.

Important Questions: Probability - Question 7

A fair dice is rolled. Probability of getting a number x such that 1 < x < 6, is

A.
0
B.
> 1
C.
between 0 and 1
D.
1

Detailed Solution: Question 7

A fair dice has six faces numbered 1, 2, 3, 4, 5, 6, and each outcome is equally likely.

Given Condition:
We need to find the probability of getting a number x such that 1 ≤ x ≤ 6.

Step 1: Number of favorable outcomes
The possible outcomes for x satisfying 1 ≤ x ≤ 6 are 1, 2, 3, 4, 5, 6. This gives a total of 6 favorable outcomes.

Step 2: Total possible outcomes
When a fair dice is rolled, there are 6 total possible outcomes.

Step 3: Probability formula

Probability = (Number of favorable outcomes) / (Total possible outcomes)

Probability = 6 / 6 = 1

Important Questions: Probability - Question 8

A die is thrown once, the probability of getting a prime number is

A.
2/3
B.
1/3
C.
1/2
D.
1/6

Detailed Solution: Question 8

When a die is rolled, there are six possible outcomes: 1, 2, 3, 4, 5, and 6. The prime numbers within this range are 2, 3, and 5, which gives us three favorable outcomes. Therefore, the probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes, resulting in 3/6 = 1/2.

Important Questions: Probability - Question 9

The sum of the probabilities of all elementary events of an experiment is p, then

A.
0 < p < 1
B.
0 > p > 1
C.
p = 1
D.
p = 0

Detailed Solution: Question 9

According to the basic axiom of probability, the sum of the probabilities of all individual outcomes in any experiment is always 1 because the sample space includes every possible outcome. Option A suggests a range that does not include 1, option B presents an invalid inequality, and option D indicates a probability of 0, which contradicts the fundamental principle that probabilities in a complete sample space must total 1.
So option C is correct

Important Questions: Probability - Question 10

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

A.
4/15
B.
2/15
C.
1/5
D.
1/3

Detailed Solution: Question 10

The numbers that is a multiple of 4 present between 1-15 are 4,8,12.
total numbers between 1 to 15=15,
the probability of getting a number that is a multiple of 4= number of favourable outcomes of event e/ total number of outcomes.
=3/15
=1/5

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