2011 H2 Mathematics Paper 2 Question 7

The Binomial Distribution

Answers

(i)

  • The probability of successfully contacting a friend is the same for each friend
  • The success of contacting a friend is independent of any other friend

(ii)

There may be different probabilities in successfully contacting different friends.
For example, a particular friend may always be using his/her phone so there is a higher chance of contacting him/her. Meanwhile, another friend often turns off his/her phone so there is a lower chance of contacting him/her.

(iii)

0.552{0.552}

(iv)

Out of syllabus

Full solutions

(i)

  • The probability of successfully contacting a friend is the same for each friend
  • The success of contacting a friend is independent of any other friend

(ii)

There may be different probabilities in successfully contacting different friends.
For example, a particular friend may always be using his/her phone so there is a higher chance of contacting him/her. Meanwhile, another friend often turns off his/her phone so there is a lower chance of contacting him/her.

(iii)

R∼B(8,0.7)R \sim \textrm{B}\left(8, 0.7\right)
P(R≥6)=1−P(R≤5)=0.552 (3 sf)  ■\begin{align*} \mathrm{P}(R \geq 6) &= 1 - \mathrm{P}(R\leq 5) \\ &= 0.552 \textrm{ (3 sf)} \; \blacksquare \end{align*}

(iv)

Out of syllabus