Probability – Assertion and Reason Questions

Q 1 :

Assertion (A) : In a cricket match, a batsman hits a boundary 9 times out of 45 balls he plays. The probability that in a given ball, he does not hit the boundary is 4/5.

Reason (R) : $P (E) + P (n o t E) = 1 .$

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.

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(1)

Total number of balls played by batsman = 45

Number of times the batsman hits the boundary = 9

Let E be the event that the batsman hits the boundary.

Now,

$P (E) = 4 / 59 = 51 $

∴P(E) + P(not E) = 1

$∴ P (n o t E) = 1 - \frac{1}{5} = \frac{4}{5}$

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

Q 2 :

Assertion (A) : When a die is rolled, the probability of getting a number which is a multiple of 3 and 5 both is zero.

Reason (R) : The probability of an impossible event is zero.

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.

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(1)

When a die is rolled, possible outcomes are 1, 2, 3, 4, 5 and 6.

The least multiple of 3 and 5 both is 15.

So, when a die is rolled it is impossible to get a number which is multiple of 3 and 5 both i.e., it is an impossible event.

We know that the probability of an impossible event is zero.

Therefore, the probability of getting a number which is a multiple of 3 and 5 both is zero.

So, both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

Q 3 :

Assertion (A) : If a box contains 5 white, 2 red and 4 black marbles, then the probability of not drawing a white marble from the box is 5/11.

Reason (R) : $P (E) = 1 - P (E),$ where E is any event.

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)
Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.

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(4)

Given, a box contains 5 white, 2 red and 4 black marbles.

Total number of marbles =5+2+4=11

Let E be the event of drawing a white marble.

$P (E) = \frac{N u m b e r o f w h i t e m a r b l e s}{T o t a l n u m b e r o f m a r b l e s} = \frac{5}{11} W e k n o w t h a t P (E) + P (E) = 1 \Rightarrow P (E) = 1 - P (E) \Rightarrow P (N o t d r a w i n g a w h i t e m a r b l e) = 1 - P (D r a w i n g a w h i t e m a r b l e) P (E) = 1 - \frac{5}{11} = \frac{6}{11}$

Therefore, Assertion (A) is false but Reason (R) is true.

Q 4 :

Assertion (A) : It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. The probability that the 2 students have the same birthday is 0.008.

Reason (R) : $P (E) + P (E) = 1,$

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.

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(1)

It is given that in a group of 3 students, the probability of 2 student not having the same birthday is 0.992.

Let the event of 2 students not having the same birthday be E. Then, P(E) = 0.992

We know that $P (E) + P (E) = 1 \Rightarrow P (E) = 1 - P (E) \Rightarrow P (E)) = 1 - 0.992 \Rightarrow P (E)) = 0.008$

So, the probability that the 2 students have the same birthday is 0.008.

Therefore, both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of (A).

Topic Question Set

Q 1 :

Assertion (A) : In a cricket match, a batsman hits a boundary 9 times out of 45 balls he plays. The probability that in a given ball, he does not hit the boundary is 4/5.

Reason (R) : $P (E) + P (n o t E) = 1 .$

Q 2 :

Assertion (A) : When a die is rolled, the probability of getting a number which is a multiple of 3 and 5 both is zero.

Reason (R) : The probability of an impossible event is zero.

Q 3 :

Assertion (A) : If a box contains 5 white, 2 red and 4 black marbles, then the probability of not drawing a white marble from the box is 5/11.

Reason (R) : $P (E) = 1 - P (E),$ where E is any event.

Q 4 :

Assertion (A) : It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. The probability that the 2 students have the same birthday is 0.008.

Reason (R) : $P (E) + P (E) = 1,$

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