Question

If the random variable \(X\sim B(4,0.5)\), then probability \(P(X\lt 3/X\geq 1)=\ldots\)

• A. \(\frac{1}{4}\)
• B. \(\frac{3}{4}\)
• C. \(\frac{1}{3}\)
• D. \(\frac{2}{3}\)

Hint:

Use P(A|B) = P(A and B)/P(B) with the binomial probabilities for n = 4, p = 0.5.

Answer 1

The Correct Option is D

Step 1: Count Outcomes
Out of $16$ equally likely outcomes, $X\geq1$ has $15$ outcomes (all except zero heads).

Step 2: Favourable
Among these, $X\lt3$ means $X=1$ or $2$, giving $4+6=10$ outcomes.

Step 3: Ratio
$\dfrac{10}{15}=\dfrac{2}{3}$.

Final Answer:
The ratio of outcomes gives 2/3. \[ \boxed{\text{(D) }\dfrac{2}{3}} \]