A bag contains 7 red marbles, 6 green marbles, 5 yellow marbles, and 2 orange marbles. Marbles are drawn twice with replacement. What is p(yellow and green)?
The probability of drawing a yellow marble on the first draw is 5/20 or 1/4. The probability of drawing a green marble on the second draw is 6/20 or 3/10. Since the draws are independent events, we can multiply their probabilities to find the probability of both events happening:
P(yellow and green) = P(yellow) x P(green)
= (1/4) x (3/10)
= 3/40
Therefore, the probability of drawing a yellow and a green marble in that order is 3/40. If the order doesn't matter, we can also find the probability of drawing a green and a yellow marble by simply multiplying the probability of the second draw by the probability of the first draw:
P(green and yellow) = P(green) x P(yellow)
= (6/20) x (5/20)
= 3/40
So the probability of drawing either a yellow and green marble or a green and yellow marble (in any order) is:
P(yellow and green or green and yellow) = P(yellow and green) + P(green and yellow)
= (3/40) + (3/40)
= 6/40
= 3/20