Assertion-Reason Questions
Q1: Assertion (A): The probability of getting a 6 in a throw of a die is \(\frac{1}{6}\). Similarly, the probability of getting a 5 is \(\frac{1}{5}\).
Reason (R): The probability of occurrence of an event varies from 0 to 1.
Step 1: Understand the probability of getting a 6 in a throw of a die.
Since a die has 6 faces, the probability of any one face (including 6) is:
\[
P(6) = \frac{1}{6}
\]Step 2: Check the probability of getting a 5 as stated in Assertion.
The probability of getting a 5 should also be:
\[
P(5) = \frac{1}{6}
\]
(because each face has equal chance)
But Assertion says \( \frac{1}{5} \), which is incorrect.
Step 3: Understand the Reason (R).
The probability of an event lies between 0 and 1 (inclusive).
\[
0 \leq P(E) \leq 1
\]
This is true.
Step 4: Conclusion:
– Assertion (A) is false because the probability of getting a 5 is incorrectly given.
– Reason (R) is true.
Answer: d. Assertion (A) is false but Reason (R) is true.
Q2: Assertion (A): In a throw of a die, the probability of getting an even number is the same as that of getting an odd number.
Reason (R): Probability of occurrence of an event E is given by
\(P\left(E\right)=\ \frac{\text{number of outcomes favourable to E}}{\text{total number of possible outcomes}}\)
Step 1: Evaluate Assertion (A).
When a standard die is thrown, the possible outcomes are \(\{1, 2, 3, 4, 5, 6\}\).
The even numbers are \(\{2, 4, 6\}\), which is \(3\) outcomes.
The odd numbers are \(\{1, 3, 5\}\), which is \(3\) outcomes.
The probabilities are both \(\frac{3}{6} = \frac{1}{2}\).
Assertion (A) is **True**.
Step 2: Evaluate Reason (R).
The formula provided is the standard definition of probability for equally likely outcomes.
Reason (R) is **True**.
Step 3: Check if Reason (R) explains Assertion (A).
The formula (R) is the exact principle used to calculate the probabilities and confirm that they are the same in assertion (A).
Reason (R) correctly explains Assertion (A).
Answer: a. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
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