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Misunderstanding Randomness

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Which of these statements do you agree with?


a) I've renumbered the faces of an ordinary die to read: 2, 2, 2, 2, 2, 9. I roll it a lot and write down the numbers; they are random numbers.

b) I flipped a coin 10 times and got all heads, something must be wrong with the coin or my throwing.

c) I've flipped a coin 10 times so far and got heads every time. It is really likely that the next one will be a tail because the tails really need to catch up.

d) I've flipped a coin 10 times so far and got heads every time. I know the next one will be heads because the coin must be biased.

e) I did 3 divided by 17 on my calculator, I got 0.1764705882... I think the decimal digits are random.

f) I pressed pi (symbol) on my calculator and got 3.141592654... My teacher told me that the decimal goes on forever without any pattern, this means the digits are random .

g) I want to know how tall I'll be when I grow up, but no-one can work it out in advance; we just have to wait and see. This means it's random.

h) The weather forecaster said there is a 30% chance of rain in my region tomorrow
- So it will rain on 30% of the region.
- It means that it'll rain for 30% of the time.
- Out of all the regions which get this warning, it'll only rain on 30% of them.
- 30% of the forecasters think it'll rain, the other 70% think it'll be sunny.

i) The weather is totally random - it's so mixed, and even if the forecasters try very hard, they don't always get it right.

j) The weather tomorrow isn't random, it depends on the weather today.

k) In the national lottery it is very likely that the balls selected will be a mixture of colours. You are more likely to win if you select numbers from a mixture of colour sets.

l) In the national lottery, you shouldn't pick a set of consecutive numbers because it's almost impossible for them to come up.

m) Ann: Here's a truly random sequence (thinking "I got them from throwing a die"...) 1, 5, 3, 4, 2, 6, 6, 3, 3, 5,...
Bob: But they're not random - there are no sevens or eights or nines!
Chris: You're both correct! Randomness is all about perception - what matters is how you view the numbers, not how they were generated.