(e) Probability and Statistics

Question 1
Describe each of the data items below as qualitative, quantitative and continuous, or quantitative and discrete.

(a)	qualitative quantitative and continuousquantitative and discrete
(b)	qualitative quantitative and continuousquantitative and discrete
(c)	qualitative quantitative and continuousquantitative and discrete
(d)	qualitative quantitative and continuousquantitative and discrete

Question 2
The number of pupils absent on each of the days of a 4-week period are given in a table below.

(a)	Complete the frequency table on the right (you may wish to do a tally table on a piece of paper). Make sure you write in a zero (0) if there are no occurences of a particular value.
	Mon Tue Wed Thu Fri Week 1 Week 2 Week 3 Week 4 Number of pupils absent each day Frequency 0       1       2       3       4       5       6       7       8       TOTAL
(b)	Display the frequency data in the bar chart above. To set the height of a bar, click the top of where the bar should be. To clear a bar, click the top again.
(c)	For the number of pupils absent each day, work out the: (i) mode (ii) median (iii) mean (iv) range

Question 3
The pie chart below illustrates the method of transport to school for pupils.

	(a)	What size is the angle in the diagram that represents CAR? °
	(b)	What size angle in the diagram represents one pupil? °
	(c)	How many pupils travel by to school? pupils
	(d)	What percentage of the pupils WALK to school? %

Question 4
Describe the events below as impossible, less than half a chance, half chance, more than half a chance, or certain.

(a)		impossibleless than half a chance half chancemore than half a chancecertain
(b)		impossibleless than half a chance half chancemore than half a chancecertain
(c)		impossibleless than half a chance half chancemore than half a chancecertain
(d)		impossibleless than half a chance half chancemore than half a chancecertain
(e)		impossibleless than half a chance half chancemore than half a chancecertain
(f)		impossibleless than half a chance half chancemore than half a chancecertain

Question 5
The probabilities of several events are marked on the probability scale below.

Work out which letter on the scale corresponds to the probability of each of these events.

(a)		AB CDEFG
(b)		AB CDEFG
(c)		AB CDEFG

In the next few questions you will need to fill in some of the answers as fractions. Do this by putting the numerator in the top box and the denominator in the bottom box, like this:

Question 6
A fair six-sided dice is thrown once. Work out the probabilities of the events below, as fractions.

(a)
(b)
(c)

Question 7
A fair coin is tossed 3 times and the results are noted.

(a)	List all the possible outcomes, using "H" for heads and "T" for tails. Each combination should only appear once and have three letters. The combinations should all be separated by commas, like this:
	The combinations are:
(b)	Write down the probability, as a fraction, of obtaining:
	(i) (ii)

Question 8
A bag contains balls. are RED and are BLUE.
One ball is taken out, its colour is noted, and it is not placed back in the bag.
A second ball is then taken from the bag, and its colour is also noted.

(a)	Complete the probabilities on the tree diagram below.
(b)	Use the tree diagram to calculate the probabilities of:
	(i) 2 RED balls (ii) exactly 1 RED ball