4. Shamrock Limited manufactures parts for smart phones. The relative frequency that a part will be made with a fault is 0 ⋅ 05. Shamrock Limited manufacture 10 000 parts each day. Work out an estimate for the number of parts each day that will not contain a fault.


5. There are six colours of marbles in a bag of 500 marbles. The colours are red, blue, green, orange, yellow and brown. 60 students randomly pick one marble from the bag, record its colour and replace it.


The results of the colours they pick are shown in the frequency table. Colour of marble


Number of times picked Relative frequency


Red 9


9 6 0 ⋅ 20 0 ⋅ 10


(i) Copy and complete the relative frequency table. (ii) Add up all the relative frequencies in the table. What do they equal?


(iii) Based on the table above, if you were the fi rst person to choose, what is the probability you would choose a red marble?


(iv) Bobby thinks a person is more likely to choose a yellow marble from this bag than any other colour. Based on the data given above, would you agree or disagree with Bobby? Justify your answer.


(v) Using the relative frequency in your completed table, estimate how many of each colour marble are in a bag of 500.


6. A drawer contains four single socks: two red socks (R), one blue sock (B) and one yellow sock (Y). Two socks are selected at random and without replacement.


(i) Copy and complete the tree diagram provided to show all outcomes of this experiment.


(ii) Calculate the probability of obtaining: (a) a red sock and a blue sock (b) any pair of socks which are the same colour (c) any pair of socks which are a diff erent colour.


(iii) What is the probability of choosing a pair of yellow socks? Justify your answer.


7. The Department of Education conducted a nationwide survey to see how many students chose Maths as their favourite subject. The sample size was increased each time. The results are listed in the table.


Sample size


Number of students choosing Maths Relative frequency


(i) Is the data collected categorical or numerical? Justify your answer.


(ii) Copy the frequency table and fi ll in the missing relative frequencies.


(iii) Copy the graph provided and draw the graph of relative frequency.


(iv) If the sample size was 5 000 students, estimate how many students you think would choose Maths as their favourite subject. Justify your answer.


30 50 100 200 500 1 000 6 10 20 45 120 250


0.2 y 0⋅4


0⋅35 0⋅3


0⋅25 0⋅2


0⋅15 0⋅1


0⋅05 x Sample size Relative frequency of Maths as favourite subject Start outcomes


R R B


R B Y


R


RR RB


Blue Green Orange Yellow Brown Total 12


21 3 60


Section A Applying our skills


103


5 Probability


Relative frequency


50 0


100 150


200 300 400 500 600 700 800 900


250 350 450 550 650 750 850 950


1 000


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