A random variable X can take any positive integer value x with probability P(X=x) = (1/2)ˣ. The probability that X is an even number is: A. 1/2 B. 1/3 C. 2/3 D. 1/4 Answer: B) 1/3 Explanation: P(Even) = P(2) + P(4) + ... = (1/2)² + (1/2)⁴ + ... This is an infinite geometric series with a = 1/4 and r = 1/4. Sum = a/(1−r) = (1/4)/(3/4) = 1/3.

imo class 12 probability

A random variable X can take any positive integer value x with probability P(X=x) = (1/2)ˣ. The probability that X is an even number is:

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A random variable X can take any positive integer value x with probability P(X=x) = (1/2)ˣ. The probability that X is an even number is:

A. 1/2
B. 1/3
C. 2/3
D. 1/4

Answer: B) 1/3

Explanation: P(Even) = P(2) + P(4) + ... = (1/2)² + (1/2)⁴ + ... This is an infinite geometric series with a = 1/4 and r = 1/4. Sum = a/(1−r) = (1/4)/(3/4) = 1/3.

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