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________________________________________________________

This question is worth 4+2+2=8 marks

We have two boxes. Box A contains two red balls and four white balls; Box B contains four red balls and one white ball. I toss a coin; if it comes down heads, I choose Box A, if it comes down tails, I choose Box B. From the chosen box I take two balls without replacement. 

a.  Draw a tree diagram to illustrate this experiment.  

b. What is the probability the two balls are of different colours?

c. What is the probability the two balls are of the same colours?

This question is a hybrid question.  Please clearly label a blank piece of paper with this question number and write your response to this question.

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________________________________________________________

This question is worth 4+6=10 marks

Weights of bags of potatoes are normally distributed with mean 26 kg. 

a. The probability that any bag weighs more than 25 kg is 0.85. Find the standard deviation of the

distribution, showing all working. (Give your answer in 4 decimal places).

b. Ten bags are chosen at random; the probability that at least

bags weigh more than 25 kg is about 82%.

Find the value of

This question is a hybrid question.  Please clearly label a blank piece of paper with this question number and write your response to this question.

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The area under the curve

is known to

be

Using the Trapezium Rule with 5 sub-intervals, find the

approximate value of

In a particular suburb, it is found that 70% of children attend state schools, while the rest attend private schools.

If groups of 40 students are chosen from this suburb, what is the average number of students in each group who attend state schools?

For two events and , ,   and

.

Find

This question is a hybrid question.  Please clearly label a blank piece of paper with this question number and write your response to this question.

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If  

In a room there are six chairs in a row, and three married couples, Mr and Mrs Andrews, Mr and Mrs Brown and

Mr and Mrs Chan. These people sit down at random. What is the probability that Mr and Mrs Andrews sit together?