In an experiment where two fair dice are rolled we observe the events that the sum of the dice are 5 and the sum of the dice is 11.

Question

i) Are these events independent? If so, why? If not, why?

ii) What is the probability of the sum of two dice is 5 and the sum of the dice is 11?

Answer 1

There are 4 ways the sum of the dice is 5: 1+4, 4+1 and 2+3 and 3+2, out of 36 possible outcomes.

There are only two ways the sum of the dice is 11: 5+6 and 6+5.

(i) The probabilities are different but one event cannot be said to cause the other. In that sense they are independent. 

(ii) The probability of the sum of 5 is 4/36=1/9. The probability of the sum of 11 is 2/36=1/18.