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Qtn No.	1	2	3	4	5	6	Total
Marks	6	6	5	6	6	6	35
Score

Question 1 Code: 9709/61/M/J/15/3, Topic: Probability

Jason throws two fair dice, each with faces numbered 1 to 6. Event A is 'one of the numbers obtained is divisible by 3 and the other number is not divisible by 3 '. Event B is 'the product of the two numbers obtained is even'.

$\text{(i)}$ Determine whether events A and B are independent, showing your working. $[5]$

$\text{(ii)}$ Are events A and B mutually exclusive? Justify your answer. $[1]$

Question 2 Code: 9709/62/M/J/15/3, Topic: Representation of data

 

In an open-plan office there are 88 computers. The times taken by these 88 computers to access a particular web page are represented in the cumulative frequency diagram.

$\text{(i)}$ On graph paper draw a box-and-whisker plot to summarise this information. $[4]$

An 'outlier' is defined as any data value which is more than $1.5$ times the interquartile range above the upper quartile, or more than $1.5$ times the interquartile range below the lower quartile.

$\text{(ii)}$ Show that there are no outliers. $[2]$

Question 3 Code: 9709/63/M/J/15/3, Topic: Discrete random variables

On a production line making cameras, the probability of a randomly chosen camera being substandard is $0.072$. A random sample of 300 cameras is checked. Find the probability that there are fewer than 18 cameras which are substandard. $[5]$

Question 4 Code: 9709/61/O/N/15/3, Topic: Representation of data

Robert has a part-time job delivering newspapers. On a number of days he noted the time, correct to the nearest minute, that it took him to do his job. Robert used his results to draw up the following table; two of the values in the table are denoted by $a$ and $b$.

$$ \begin{array}{|l|c|c|c|c|} \hline \text{Time ( t minutes)} & 60-62 & 63-64 & 65-67 & 68-71 \\ \hline \text{Frequency (number of days)} & 3 & 9 & 6 & b \\ \hline \text{Frequency density} & 1 & a & 2 & 1.5 \\ \hline \end{array} $$

$\text{(i)}$ Find the values of $a$ and $b$. $[3]$

$\text{(ii)}$ On graph paper, draw a histogram to represent Robert's times. $[3]$

Question 5 Code: 9709/62/O/N/15/3, Topic: Probability

One plastic robot is given away free inside each packet of a certain brand of biscuits. There are four colours of plastic robot (red, yellow, blue and green) and each colour is equally likely to occur. Nick buys some packets of these biscuits. Find the probability that

$\text{(i)}$ he gets a green robot on opening his first packet, $[1]$

$\text{(ii)}$ he gets his first green robot on opening his fifth packet. $[2]$

Nick's friend Amos is also collecting robots.

$\text{(iii)}$ Find the probability that the first four packets Amos opens all contain different coloured robots. $[3]$

Question 6 Code: 9709/63/O/N/15/3, Topic: Probability

Ellie throws two fair tetrahedral dice, each with faces numbered $1,2,3$ and 4. She notes the numbers on the faces that the dice land on. Event $S$ is 'the sum of the two numbers is 4'. Event $T$ is 'the product of the two numbers is an odd number'.

$\text{(i)}$ Determine whether events $S$ and $T$ are independent, showing your working. $[5]$

$\text{(ii)}$ Are events $S$ and $T$ exclusive? Justify your answer. $[1]$