Knowing Chance

- 1 August 1991

1. A couple have had five girls in a row. What is their next baby likely to be? (a) boy, (b) girl, (c) either equally likely.

2. What is 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 (guess rather than work it out mathematically).

3. You are betting on heads on the toss of a coin. After a run of 10 heads are your chances of a win on the next throw (a) increased, (b) decreased, (c) the same?

4. A packet contains 10 mint and 10 chocolate flavour toffees. You pull out 10 and eight of them are chocolate. What are you most likely to get next time? (a) chocolate, (b) mint, c) either.

5. Multiply 8x7x6x5x4x3x2x1.

6. You are betting to get heads on the toss of a coin. After a run of five tails is the chance of winning next time (a) increased, (b) decreased, (c) the same?

7. A packet contains pink and yellow sweets in unknown proportion. You pull out 10 and eight of them are yellow. What colour are you more likely to get next (a) pink, (b) yellow, (c) either.

8. How many people do you need to have at a party to have 50:50 chance that two have the same birthday?

9. Using only the numbers one to five make a list of 100 numbers in random order.

ANSWERS

1. b orc 2. 40,320 3. c 4. b 5. 40,320 6. c 7. b 8. 22

If you got questions 1, 3 or 6 wrong you are falling for the “Gambler’s Fallacy”, believing in the so-called “law of averages”.

Questions 2 and 5 are the same but people usually underestimate even more for question 2.

For question 8, people usually give much higher answers but think of how many possible pairs of people there will be.

In question 9, a truly random string should contain about 20 repeats of the same number. How many did you have? (Three in a row counts as two repeats.)