## Sunday, June 06, 2010

### A matter of chance

Here is a puzzle. You have to guess a number from 1 to 4. Each day the correct answer is drawn. You have 1 out of 4 chance of getting it right. You repeat this exercise for 6 days. What is the probability (chance) of getting the right number for 6 days, 5 days, 4 days, 3 days, 2 days, 1 day and 0 day? Please show in percentages to 2 decimal places. The total must add up to 100%

Tan Kin Lian said...

The first correct answer was submitted by Yun Chung Lim at 10.36 pm. Congratulations.

Dear Mr Tan

Here's my solution to your post. Let X be the no. of days we choose the number correctly. Then it can be modelled as a Binomial(6, 0.25) random variable. Therefore, we get

P(X=0) = 6C0 x (0.25)^0 x (1-0.25)^6 = 17.8%
P(X=1) = 35.60%
P(X=2) = 29.66%
P(X=3) = 13.18%
P(X=4) = 3.30%
P(X=5) = 0.44%
P(X=6) = 0.02%

The rounded figures (to 2 decimal places) sum up to 100%.
Yun Ching

Tan Kin Lian said...

After Jun Ching, another 4 people submitted the correct answers.