Solution — 2018 Question 6 Binomial Distribution

(a)

Let $X$ represent the number of people who have blood group A out of $6.$

$X \sim B (6, 0.4)$

$\begin{matrix} P (X = 2) & = 0.311 04 \\ = 0.311 ∎ (to 3 s.f.) \end{matrix}$

[probability of X = 2]

(b)

Let $Y$ represent the number of people who do not have blood group A out of $6.$

$Y \sim B (6, 0.6)$

$\begin{matrix} P (Y \geq 4) & = 1 - P (Y \leq 3) \\ = 1 - 0.455 68 \\ = 0.544 32 \\ = 0.544 ∎ (to 3 s.f.) \end{matrix}$

[probability of Y \geq 4]