Question

A die is thrown 600 times. These results are obtained.

1 Do the results indicate the die is biased?
2 Justify your answer.
3 Use the data to work out the probability of the die landing on:
a 1, b 3, c 4, d 6
4 If the die were fair how many times would you expect it to land on each
number if it were thrown 600 times?

Answer 1

A die is thrown 600 times and the results are:

• 1 - 102, 2 - 112, 3 - 181, 4 - 31, 5 - 82, 6 - 92

1) There is indication of the die being biased.

2) It becomes evident number 3 is landed 181 times and number 4 is landed 31 times, whilst we would expect about 100 outcomes for each number.

3) Probabilities

• probability = favorable outcomes / total outcomes

• a) P(1) = 102/600 = 0.17 or 17%

• b) P(3) = 181/600 = 0.30 or ~ 30%

• c) P(4) = 31/600 = 0.05 or ~ 5%

• d) P(6) = 92/600 = 0.1533 or ~ 15%

4) The theoretical probability is same for each number:

• P = 1/6*600 = 100 times