Question:
A fair die is thrown at random. Let A be the event that the number obtained on the die is a non-even prime number and B be the event that the number obtained on the die is an odd number.
Let \(p:P(A) = \frac{1}{3}\), \(q\) : A and B are independent events.
Then the truth values of statements \(p\) and \(q\) respectively are.....
A fair die is thrown at random. Let A be the event that the number obtained on the die is a non-even prime number and B be the event that the number obtained on the die is an odd number.
Let \(p:P(A) = \frac{1}{3}\), \(q\) : A and B are independent events.
Then the truth values of statements \(p\) and \(q\) respectively are.....
Let \(p:P(A) = \frac{1}{3}\), \(q\) : A and B are independent events.
Then the truth values of statements \(p\) and \(q\) respectively are.....
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List the favourable outcomes of A and B, then test P(A and B) = P(A)P(B).
Updated On: Oct 1, 2026
- T , T
- T , F
- F , T
- F , F
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
A = non-even prime numbers on a die = \(\{3, 5\}\) (2 is prime but even). B = odd numbers = \(\{1, 3, 5\}\).
Step 2: Statement p:
\(P(A) = \dfrac26 = \dfrac13\), so \(p\) is TRUE.
Step 3: Statement q:
\(A \cap B = \{3, 5\}\), so \(P(A\cap B) = \dfrac13\).
\(P(A)P(B) = \dfrac13\cdot\dfrac12 = \dfrac16\).
Since \(\dfrac13 \neq \dfrac16\), the events are not independent, so \(q\) is FALSE.
Step 4: Result:
The truth values are T, F. Option (B).
Final Answer:
p is true, but A and B are not independent. \[ \boxed{\text{(B) }\text{T, F}} \]
A = non-even prime numbers on a die = \(\{3, 5\}\) (2 is prime but even). B = odd numbers = \(\{1, 3, 5\}\).
Step 2: Statement p:
\(P(A) = \dfrac26 = \dfrac13\), so \(p\) is TRUE.
Step 3: Statement q:
\(A \cap B = \{3, 5\}\), so \(P(A\cap B) = \dfrac13\).
\(P(A)P(B) = \dfrac13\cdot\dfrac12 = \dfrac16\).
Since \(\dfrac13 \neq \dfrac16\), the events are not independent, so \(q\) is FALSE.
Step 4: Result:
The truth values are T, F. Option (B).
Final Answer:
p is true, but A and B are not independent. \[ \boxed{\text{(B) }\text{T, F}} \]
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