Question

Three dice are thrown, one red, one blue, and one green. Show that the events A={the red die shows an even number} and B={the sum of the numbers on the blue and green dice is even} are independent.

Answer 1

this can be seen intuitatively that as outcome on red dice does not depend on outcome on green and blue dice therefore event A and B should be independent

Mathematically)

P(A)=3/6 =1/2 (as there are three even numbers out of 6)

P(B)=18/36 (as there are 18 combinations are even and other 18 are odd from 36 combination of blue and green dice)

P(A n B)=P(even on red and sum of blue and green dice is even number)=54/216 (as there are 54 ways out of 216 ways)

as P(A n B)=P(A)*P(B) ;therefore event A and B are independent