A jar contains 3 red and 2 white marbles. 2 marbles are picked without
replacement.(1) The probability of picking two red marbles
(2) The probability of picking exactly one red and one white marble
A. (1) > (2)
B. (1) < (2)
C. (1) = (2)
The question doesn't mention anything about picking the marbles one by one. So should I assume that 2 marbles are picked simultaneously? If so, please correct me if I'm not wrong, the answer is C since both quantities are 3/10 because:
(1) (3/5) x (2/4) = 3/10
(2) (2/5) x (3/4) = 3/10
I appreciate your help!
Best Answer
Without replacement means one-by one. The colour of the first influences the probability of the colour of the second. So consider it as two discrete events, picking of the first ball, and then picking the second ball
$$P(2R) = \frac{3}{5}.\frac{2}{4} = \frac{3}{10}$$
$$P(1R,1W) = \frac{3}{5}.\frac{2}{4} + \frac{2}{5}.\frac{3}{4} = \frac{6}{10}$$