Assertion (A) & Reason (B) MCQ

MCQ 11 Mark

Assertion (A): A die is thrown once and the probability of getting an even number is $\frac{2}{3}$.
Reason (R): The sample space for even numbers on a die is $\{2,4,6\}$

A
A is true, R is false
✓
A is false, R is true
C
Both A and R are true
D
Both A are R are false.

Answer

Correct option: B.

A is false, R is true

(b) A is false, R is true
Explanation:
In assertion, when a dice is thrown the total outcomes $=6$
Even numbers $=\{2,4,6\}$ i.e. 3
Required probability $=\frac{3}{6}-\frac{1}{2}$
So, assertion is false
In reason part, the even number on a dice is
$\{2,4,6\}$

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MCQ 21 Mark

Assertion: If a die is thrown, the probability of getting a number less than 4 and greater than 3 is zero.
Reason: Probability of an impossible event is zero.

✓
Both assertion and reason are correct and reason is the correct explanation of assertion.
B
Both assertion and reason are correct but reason is not the correct explanation of assertion.
C
Assertion is correct but reason is incorrect.
D
Assertion is incorrect but reason is correct.

Answer

Correct option: A.

Both assertion and reason are correct and reason is the correct explanation of assertion.

(a) Both assertion and reason are correct and reason is the correct explanation of assertion.
Explanation:
Getting a number less than 4 and greater than 3 on a single time thrown die is a impossible event. We know that probability of an impossible event is zero.

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MCQ 31 Mark

Assertion : It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992 , then the probability that the 2 students have the same birthday is 0.128 .
Reason) : If $n(A)=1$ and $n(S)=13$, then $P(A)=1 / 13$

A
Both assertion and reason are correct and reason is the correct explanation of assertion.
B
Both assertion and reason are correct but reason is not the correct explanation of assertion.
C
Assertion is correct but reason is incorrect.
✓
Assertion is incorrect but reason is correct.

Answer

Correct option: D.

Assertion is incorrect but reason is correct.

(d) Assertion is incorrect but reason is correct.
Explanation:
For assertion,
Let E be the event of having same birthday.
$\therefore E ^{\prime}$ be the event of not having the same birthday.
Given $P\left(E^{\prime}\right)=0.992$
Since we know that
$\begin{array}{l}P(E)+P\left(E^{\prime}\right)=1 \\
\Rightarrow P(E)=1-P\left(E^{\prime}\right) \\
\Rightarrow P(E)=1-0.992 \\
=0.008\end{array}$
So, assertion is incorrect.
For reason,
Given $n(A)=1$ and $n(S)=13$, then $P ( A )=\frac{n(A)}{n^{(S)}}=\frac{1}{13}$
So, reason is correct.

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Mathematics Assertion (A) & Reason (B) MCQ

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