Answer:

The probability of picking a blue marble on the first draw is 6/21, since there are 6 blue marbles out of a total of 21 marbles.

After the blue marble is picked and not returned, there are 20 marbles left, with 9 red, 4 yellow, and 2 green marbles. The probability of picking a pink (assuming pink means a red marble) on the second draw is 9/20, since there are 9 red marbles out of 20 left.

To find the probability of both events happening, we multiply the probability of the first event by the probability of the second event:

(6/21) x (9/20) = 54/420 = 9/70

Therefore, the probability of picking a blue marble on the first draw and a pink marble on the second draw is 9/70.

Answer:

27/190 (Quick Answer)

Step-by-step explanation:

The probability of picking a blue marble on the first draw is the number of blue marbles divided by the total number of marbles:

P(blue on first draw) = 6/(6+9+4+2) = 6/21

Since the first marble is not returned, there will be one less marble in the bag for the second draw. The probability of picking a pink marble on the second draw depends on whether or not a blue marble was picked on the first draw.

If a blue marble was picked on the first draw, there will be 5 blue marbles left in the bag, out of a total of 20 marbles:

P(pink on second draw given blue on first draw) = 9/20

If a blue marble was not picked on the first draw, there will still be 6 blue marbles left in the bag, out of a total of 19 marbles:

P(pink on second draw given not blue on first draw) = 9/19

To find the overall probability of picking a blue marble on the first draw and a pink marble on the second draw, we multiply the probabilities:

P(blue on first draw and pink on second draw)

= P(blue on first draw) * P(pink on second draw given blue on first draw)

+ P(not blue on first draw) * P(pink on second draw given not blue on first draw)

= (6/21) * (9/20) + (15/21) * (9/19)

= 54/380

= 27/190