See image for question. Question Continuation:
a. both of them winning their respective States.
b. both of them lose in their respective States.
c. at least one of them wins in his state.​

Question 1

Total number of marbles = 5 + 7 + 8 = 20

(a)

P(red, red) = 5/20*4/19 = 1/19

(b)

P(white and blue) = P(white, blue or blue, white) = 7/20*8/19 + 8/20*7/19 = 14/95 + 14/95 = 28/95

(c)

P(both same colour) = P(red,red or blue,blue or white,white) = 1/19 + 8/20*7/19 + 7/20*6/19 = (20 + 56 + 42)/380 = 118/380 = 59/190

Question 2

P(A) = 2/9P(B) = 4/11

(a)

P(A and B) = 2/9 * 4/11 = 8/99

(b)

P(not A and not B) = (1 - P(A))(1 - P(B)) = 7/9*7/11 = 49/99

(c)

P(A or B) = 1 - P(not A and not B) = 1 - 49/99 = 50/99

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