Question

You wish to play a three-number lottery with your favorite data 8, 2 and 5. After a number is drawn, the number is placed back in the container for the next draw. What is the probability that the three winning numbers will be 8, 2 and 5? Are the numbers independent of each other? How would the probability change if no repetition is allowed?

Answer 1

a) The probability that the three numbers drawn are 8, 2 and 5 in the same order is computed here as:
= 1 / Total number of draws possible

= 1 / 3*3*3

= 1/27

Therefore 1/27 is the required probability here.

b) As we are doing the drawing of numbers here with replacement, that is the number if kept back after drawing one number for the future draws, therefore yes the numbers here are independent of each other.

c) Given that repetition is not allowed, the probability would be computed as:
= 1 / Total number of permutations of 3 numbers

= 1/ 3!

= 1/6

Therefore 1/6 is the required probability here.