2015 H2 Mathematics Paper 2 Question 6

The Binomial Distribution

Answers

{0.224}

Out of syllabus

{0.824}

Let

{X}

denote the r.v. of the number of red sweets in a small packet of

{10}

X \sim \textrm{B}\left(10, 0.25\right)

\begin{align*} \mathrm{P}(X \geq 4) &= 1 - \mathrm{P}(X\leq 3) \\ &= 0.224 \textrm{ (3 sf)} \; \blacksquare \end{align*}

Out of syllabus

Let

{Y}

denote the r.v. of the number of red sweets in a large packet of

{100}

Y \sim \textrm{B}\left(100, 0.25\right)

\begin{align*} \mathrm{P}(Y \geq 30) &= 1 - \mathrm{P}(Y\leq 29) \\ &= 0.14954 \end{align*}

Let

{W}

denote the r.v. of the number of packets containing at least 30 red sweets out of

{15}

W \sim \textrm{B}\left(15, 0.14954\right)

\begin{align*} \mathrm{P}(W \leq 3) &= 0.824 \textrm{ (3 sf)} \; \blacksquare \end{align*}