Please solve and show work and type it up.

5 ) A die is loaded so that the probability of each face turning up is proportional to the number on that face. If we throw this die once, find the probability of getting an even number Hint: First, find the probability for each face If P ( 1 ) = x, then P ( 2) = 2x, P 13)= 3x, P(4)= 4x, P( 5 ) = 5 x and P(6) = 6X. What is the sum of all probabilities? Find x. Then find the probability of getting an even number. 6) ( Extra Credit ) If A and B are two events with P (BIA ) = = and P( A complement ) = = find P(BNA )