Question

For a binomial distribution, n = 5.
If P (X = 4) = P (X = 3), then P (X > 2) is

• A. 0.69
• B. 0.97
• C. 0.21
• D. 0.79

Answer 1

Answer: (D)

0.79

$n=5P(X=4){=}^5{C}_4{p}^{4}q=5p^{4}qP(X=3){=}^5{C}_3{p}^3{q}^2=10p^3{q}^{2}P(X=3)=P(X=4)⟹p=2qp+q=1q=\frac{1}{3},p=\frac{2}{3}P(X>2)=P(X=3)+P(X=4)+P(X=5)10{\left(\frac{2}{3}\right)}^3{\left(\frac{1}{3}\right)}^2+5{\left(\frac{2}{3}\right)}^4\left(\frac{1}{3}\right)+{\left(\frac{2}{3}\right)}^5=\frac{192}{243}=0.79$