8 The box and whisker plot below summarises the weights in grams of the 20 chocolates in a box.
\includegraphics[max width=\textwidth, alt={}, center]{6015ae6c-bf76-4a0c-af0f-5c53f9c5ed2a-4_287_1177_319_427}
- Find the interquartile range of the data and hence determine whether there are any outliers at either end of the distribution.
Ben buys a box of these chocolates each weekend. The chocolates all look the same on the outside, but 7 of them have orange centres, 6 have cherry centres, 4 have coffee centres and 3 have lemon centres.
One weekend, each of Ben's 3 children eats one of the chocolates, chosen at random.
- Calculate the probabilities of the following events.
A: all 3 chocolates have orange centres
\(B\) : all 3 chocolates have the same centres - Find \(\mathrm { P } ( A \mid B )\) and \(\mathrm { P } ( B \mid A )\).
The following weekend, Ben buys an identical box of chocolates and again each of his 3 children eats one of the chocolates, chosen at random.
- Find the probability that, on both weekends, the 3 chocolates that they eat all have orange centres.
- Ben likes all of the chocolates except those with cherry centres. On another weekend he is the first of his family to eat some of the chocolates. Find the probability that he has to select more than 2 chocolates before he finds one that he likes.
\section*{END OF QUESTION PAPER}
\section*{OCR
Oxford Cambridge and RSA}