Solution — 2020 Question 7 Binomial Distribution

(a)

Let $X$ represent the number of oranges that are not ripe in a bag of $12.$

$X \sim B (12, 0.15)$

$\begin{matrix} P (X = 1) & = 0.301 22 \\ = 0.301 ∎ (to 3 s.f.) \end{matrix}$

[probability of X = 1]

(b)

$\begin{matrix} P (X > 3) & = 1 - P (X \leq 3) \\ = 1 - 0.907 79 \\ = 0.092 206 \\ = 0.0922 ∎ (to 3 s.f.) \end{matrix}$

[probability of X > 3]

(c)

$\begin{matrix} P (both bags at reduced price) \\ = 0.092 206 (0.092 206) \\ = 0.00850 ∎ \end{matrix}$

(d)

Let $Y$ represent the number of bags sold at the reduced price out of $20.$

$Y \sim B (20, 0.092 206)$

$\begin{matrix} P (Y < 4) & = P (Y \leq 3) \\ = 0.893 66 \\ = 0.894 ∎ (to 3 s.f.) \end{matrix}$

[probability of Y < 4]