Solution — 2018 Question 6 Binomial Distribution

(a)

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

$ ParseError: Can't use function '$' in math mode at position 1: $̲ X \sim \mathrm{B} \left( 6, 0.4 \right)

\begin{align*} \mathrm{P}\left(X = 2\right) &= 0.311\,04 \\ &= 0.311\; \QED \text{ (to 3 s.f.)} \end{align*}$$ ParseError: {align*} can be used only in display mode.

[probability of X = 2]

(b)

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

$ ParseError: Can't use function '$' in math mode at position 1: $̲ Y \sim \mathrm{B} \left( 6, 0.6 \right)

\begin{align*} \mathrm{P}\left(Y \geq 4\right) &= 1 - \mathrm{P}\left(Y \leq 3\right) \\ &= 1 - 0.455\,68 \\ &= 0.544\,32 \\ &= 0.544\; \QED \text{ (to 3 s.f.)} \end{align*}$$ ParseError: {align*} can be used only in display mode.

[probability of Y \geq 4]