(Easy) Probability of boxes and marbles

Question

 Box A contains two red marbles and six blue marbles. 

 Box B contains five red marbles, three yellow marbles and six blue marbles. Box C contains eight red marbles, six yellow marbles in 4 blue marbles.

 

The box is chosen at random and a marble is selected at random from the box.

 

Find the probability that

a) Box B is chosen,

b) Box A is chosen and the marble selected is yellow

c) Box C is chosen and the marble selected is red 

d) the marble selected is blue. 

Answer 1

3 boxes

A has 2 red 6 blue

B has 5 red 3 yellow 6 blue

C has 8 red 6 yellow 4 blue

randomly pick a marble

a) P(B) = 1/3

b) P(A&yellow) = (1/3)(0/3) = zero

c) P(C&red) = (1/3)(8/18 = 4/27

d) P(blue) = (1/3)(6/8 +6/14 + 4/18) = (1/3)(3/4+3/7+2/9)= (1/3)((189+108+56)/(28)(9)) = 353/28(27)=353/756