A bag contains contains 20 blue marbles, 20 green marbles, and 20 red marbles.
Two marbles are drawn one after the other. no replacement
Using selection (combinations), find the probability of:
(a) drawing two marbles of the same colour
(b) drawing a blue and a green marble
(c) drawing a blue or a green marble
Would the sample space be P(60,2) or C(60,2)
Best Answer
The question asks for combinations, but permutation seems more intuitive to me in this question, as the order of the marbles being drawn has to be taken into account.
I would use P(60,2) as the sample space. By doing so, I have to treat all 60 marbles as distinctive:
Blue: Marble 1, Marble 2, Marble 3..., Marble 20
Green: Marble 21, Marble 22, Marble 23..., Marble 40
Red: Marble 41 to Marble 60
(a) drawing two marbles of the same colour
$Probability = \frac{20P2+20P2+20P2}{60P2}$
(b) drawing a blue and a green marble
$Probability = \frac{(20P1*20P1)+(20P1*20P1)}{60P2}$
(c) drawing a blue or a green marble
$Probability = \frac{(20P1*40P1)+(20P1*40P1)}{60P2}$
Look forward to an answer that uses combinations instead.