Probability

Class 9 > Math > NCERT > Probability

Assertion and Reason for Probability Class 9 Math

Important Questions

A

Directions : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Answer

(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

1

Assertion (A): Two coins are tossed. Number of elements in the sample space is 4.
Reason (R): When a coin is tossed n times then the number of elements in its sample space is 2n .

Answer

(a) Both assertion and reason are true and reason is the correct explanation of assertion.

2

Assertion (A): If E1, E2, .........., En are n elementary events associated to a random experiment, then P(E1) + P(E2) + …. + P(En) = 1
Reason (R): For any event ‘A’ associated to an experiment, we have – 1 ≤ P(A) ≤ 1

Answer

(c) Assertion is correct but Reason is incorrect.

3

Assertion (A): A die is thrown. Let E be the event that number appears on the upper face is less than 1, then P(E) = 1/6
Reason (R): Probability of impossible event is 0.

Answer

(d) Assertion is false but reason is true.


When a die is thrown, then number of outcomes are 1, 2, 3, 4, 5, 6
P(number appear on the upper face is less than 1) = 0

4

Assertion (A): A coin is tossed two times. Probability of getting at least two heads is ¼ .
Reason (R): When a coin is tossed two times, then the sample space is {HH, HT, TH, TT}

Answer

(a) Both assertion and reason are true and reason is the correct explanation of assertion.


Number of total outcomes when a coin is tossed 2 times i.e., {HH, HT, TH, TT} = 4
P (getting at least two heads) = ¼

5

Assertion (A): Tossing a coin 50 times is called an event.
Reason (R): The possible outcomes of an experiment are called events.

Answer

(d) Assertion is incorrect but Reason is correct.


Tossing a coin 50 times is called an experiment.

6

Assertion (A): In a class there are x boys. and y girls, A student is selected at random, then the probability of selecting a girl is y/x .
Reason (R): Probability of an event E of an experiment is ratio of the number of trials in which event E has happened to the total number of trials.

Answer

(d) Assertion is incorrect but Reason is correct.


P (selecting a girl) = y/(x + y)

7

Assertion (A): A fair die is rolled. Then the probability of getting an even number is ½ and probability of getting an odd number is ½ .
Reason (R): Possible outcomes when a fair die is rolled is (1, 2, 3, 4, 5, 6).

Answer

(a) Both assertion and reason are true and reason is the correct explanation of assertion.


Possible outcomes when a die is thrown = {1, 2, 3, 4, 5, 6}
P (getting an odd number) = 3/6 = ½
P (getting an even number) = 3/6 = ½

8

Assertion (A): Two well balanced dice are rolled and the numbers that turn up are observed. Then the number of elements in sample space is 12.
Reason (R): When two dice are rolled, number of elements in sample space is 6 × 6.

Answer

(d) Assertion is false but reason is true.

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