# Test 2. Common entrance exams,11+/13+

by Sara

Here is our second test for you to practice for the common entrance exams. Questions by courtesy of Galore Park for the ISEB board.

At a funfair there was a stall where people could roll a die. (courtesy of Galore Park)

ROLL THE DIE

£1 to enter

Choose your own die

Roll a six and win £6

Tim thought about this and decided to have six tries, knowing that he'd spend £6, and thinking that he'd be bound to win £6 on one of his six rolls, so he couldn't lose! Since blue is his favourite colour, he choose a blue die and rolled it six times.

He was dismayed to discover he didn't roll a single six. The numbers he rolled were: 5, 2, 3, 1, 2, 4

Tim claimed that the die must be biased!

(a) (i) What do you think about Tim's strategy?

(ii) Do you think the die was biased?

The stall holder told Tim to choose another die and try again, free of charge. This time Tim chose a large gold coloured die and rolled 1 six times.

(b) Do you think that this second die is fair?

(c) Describe a sensible way to finding out if a die is biased.

(d) Suggest a way in which the stall holder can be fairly certain that he will make money.

Give an example of an event which:

(a) is impossible

(b) is very unlikely

(c) is unlikely

(d) has an even chance of happening

(e) is likely

(f) is very likely

(g) is certain to happen