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CBSE Class 10 Standard Math 2026 All Sets Solved Paper

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Question : 20 of 20
Marks: +1, -0
Assertion (A) : If probability of happening of an event is 0.2p, p > 0, then p can’t be more than 5.
Reason (R) : P(E) = 1 − P(E) for an event E.
Solution:  
Probability of any event E always lies between 0 and 1 inclusive (0P(E)1)(0 \leq P(E) \leq 1).
The sum of probability of occurrence and non-occurrence of an event is 1.
Assertion (A): Given P(E) = 0.2p.
Since P(E) \leq 1:
0.2p10.2p \leq 1
p  10.2p \leq \;\frac{1}{0.2}
p5p \leq 5
So, p cannot be more than 5. (A) is true
Reason (R): It is a fundamental property of probability that P(E)+P(E)=1, so P(E)=1P(E)P(E) + P(\overline{E}) = 1, \text{ so } P(\overline{E}) = 1 - P(E). (R) is true.
Connection: While both are true, the reason for p \leq 5 is the definition of the range of probability (0P(E)1)(0 \leq P(E) \leq 1), not specifically the formula for the complement event. Thus, (R) is not the explanation for (A).
Both (A) and (R) are true, but (R) is not the correct explanation of (A).
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