Question

Two numbers are selected without replacement from the first six positive integers. Let X denote the number of prime numbers obtained. The mean value of X is .......

• A. \(0.6\)
• B. \(1\)
• C. \(1.2\)
• D. \(0.8\)

Hint:

Find the probability distribution of X for two selections from 1 to 6 and compute the expected value.

Answer 1

The Correct Option is B

Step 1: Use Linearity
Let $X=X_{1}+X_{2}$, where $X_{i}$ indicates that the $i$th number is prime.

Step 2: Probabilities
By symmetry each pick is prime with probability $\dfrac{3}{6}=\dfrac{1}{2}$.

Step 3: Add
$E(X)=\dfrac{1}{2}+\dfrac{1}{2}=1$.

Final Answer:
The expected number of primes is 1. \[ \boxed{\text{(B) }1} \]