Abox contains 8 green and 4 blue marbles. two
marbles are selected (at once with no replacement).
find the expected number of green marbles among
the selected ones.
(a) 1
(b) 1/3
(c) 2/3
(d) 1/2
(e) 4/3
(f) none of the above

Option (f). None of the above.

Step-by-step explanation:

As it has been in the question that in a box number of green and blue marbles are 8 and 4 respectively.

Since marbles are selected at once with no replacement, we have to find the expected numbers of green marbles among the selected ones.

Total numbers of marbles = green + blue = 8 + 4 = 12

P (green) for selection of first marble = 8/12 = 2/3

Now for the selection of second marble which should be green will be

P'(green) = 7/11 ( here number of green marbles remaining = 7 and total green plus blue marbles is = 7 + 4 = 11

Now for these two individual events probability for both the marbles of being green will be = P(green) × P'(green) = 2/3 × 7/11 = 14/33

Therefore answer is Option (f) None of the above.