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Answer: (a) \(\frac{3}{8}\) (b) \(\frac{5}{16}\) (c) \(\frac{11}{16}\)

\(p=P(\text{odd})=\frac{3}{6}=\frac{1}{2}\), \(q=\frac{1}{2}\), \(n=4\). \(X\sim B\left(4,\frac{1}{2}\right)\): \(P(X=x)={}^4C_x\left(\frac{1}{2}\right)^4=\frac{{}^4C_x}{16}\).

(a) \(P(X=2)=\frac{6}{16}=\frac{3}{8}\).

(b) \(P(X\ge 3)=P(3)+P(4)=\frac{4+1}{16}=\frac{5}{16}\).

(c) \(P(X\le 2)=P(0)+P(1)+P(2)=\frac{1+4+6}{16}=\frac{11}{16}\).

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report
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