Edexcel AS Paper 2 (AS Paper 2) 2021 November

1.
\includegraphics[max width=\textwidth, alt={}, center]{6dfefd72-338f-40be-ac37-aef56bfaccaa-02_399_743_248_662} The Venn diagram, where \(p\) is a probability, shows the 3 events \(A , B\) and \(C\) with their associated probabilities.

1. Find the value of \(p\).
2. Write down a pair of mutually exclusive events from \(A , B\) and \(C\).

1. The partially completed table and partially completed histogram give information about the ages of passengers on an airline.

There were no passengers aged 90 or over. \includegraphics[max width=\textwidth, alt={}, center]{6dfefd72-338f-40be-ac37-aef56bfaccaa-04_1173_1792_721_139}

1. Complete the histogram.
2. Use linear interpolation to estimate the median age. An outlier is defined as a value greater than \(Q _ { 3 } + 1.5 \times\) interquartile range.
   Given that \(Q _ { 1 } = 27.3\) and \(Q _ { 3 } = 58.9\)
3. determine, giving a reason, whether or not the oldest passenger could be considered as an outlier.
   (2)

1. Helen is studying one of the qualitative variables from the large data set for Heathrow from 2015.

She started with the data from 3rd May and then took every 10th reading.
There were only 3 different outcomes with the following frequencies

1. State the sampling technique Helen used.
2. From your knowledge of the large data set
   1. suggest which variable was being studied,
   2. state the name of outcome \(A\). George is also studying the same variable from the large data set for Heathrow from 2015. He started with the data from 5th May and then took every 10th reading and obtained the following

      Outcome	\(A\)	\(B\)	\(C\)
      Frequency	16	1	1

      Helen and George decided they should examine all of the data for this variable for Heathrow from 2015 and obtained the following

      Outcome	\(A\)	\(B\)	\(C\)
      Frequency	155	26	3

3. State what inference Helen and George could reliably make from their original samples about the outcomes of this variable at Heathrow, for the period covered by the large data set in 2015.

1. A nursery has a sack containing a large number of coloured beads of which \(14 \%\) are coloured red.

Aliya takes a random sample of 18 beads from the sack to make a bracelet.

1. State a suitable binomial distribution to model the number of red beads in Aliya’s bracelet.
2. Use this binomial distribution to find the probability that
   1. Aliya has just 1 red bead in her bracelet,
   2. there are at least 4 red beads in Aliya’s bracelet.
3. Comment on the suitability of a binomial distribution to model this situation. After several children have used beads from the sack, the nursery teacher decides to test whether or not the proportion of red beads in the sack has changed. She takes a random sample of 75 beads and finds 4 red beads.
4. Stating your hypotheses clearly, use a 5\% significance level to carry out a suitable test for the teacher.
5. Find the \(p\)-value in this case.

1. Two bags, \(\mathbf { A }\) and \(\mathbf { B }\), each contain balls which are either red or yellow or green.

Bag A contains 4 red, 3 yellow and \(n\) green balls.
Bag \(\mathbf { B }\) contains 5 red, 3 yellow and 1 green ball.
A ball is selected at random from bag \(\mathbf { A }\) and placed into bag \(\mathbf { B }\).
A ball is then selected at random from bag \(\mathbf { B }\) and placed into bag \(\mathbf { A }\).
The probability that bag \(\mathbf { A }\) now contains an equal number of red, yellow and green balls is \(p\). Given that \(p > 0\), find the possible values of \(n\) and \(p\).