A small pouch contains 8 black marbles 5 white marbles and 12 red marbles Find the probability of picking a red then a black marble if you do not replace the first marble

prob(red, then black) = (12/25)(8/24) =

To find the probability of picking a red marble first and then a black marble without replacing the first marble, we need to consider two events: picking a red marble and picking a black marble.

Let's first calculate the probability of picking a red marble:

Total number of marbles = 8 (black) + 5 (white) + 12 (red) = 25
Number of red marbles = 12

Picking a red marble = Number of red marbles / Total number of marbles = 12 / 25 = 0.48 or 48%

Now, after picking a red marble, there are 11 red marbles left. The total number of marbles has decreased to 24.

Next, let's calculate the probability of picking a black marble from the remaining marbles:

Total number of marbles remaining = 24
Number of black marbles = 8

Picking a black marble = Number of black marbles / Total number of marbles = 8 / 24 = 0.33 or 33%

To find the probability of both events happening, we multiply the individual probabilities together:

Probability of picking a red then a black marble = Probability of picking a red marble * Probability of picking a black marble
= 0.48 * 0.33 = 0.1584 or 15.84%

To find the probability, we first need to determine the total number of marbles in the pouch. The total number of marbles is obtained by adding the number of black, white, and red marbles together:

Total number of marbles = number of black marbles + number of white marbles + number of red marbles
Total number of marbles = 8 + 5 + 12
Total number of marbles = 25

Next, we determine the probability of picking a red marble first. Since there are 12 red marbles out of a total of 25:

Probability of picking a red marble first = Number of red marbles / Total number of marbles
Probability of picking a red marble first = 12 / 25

Finally, to find the probability of picking a black marble after picking a red marble without replacement, we need to consider that now there are 24 marbles left in the pouch, including 7 black marbles and 5 red marbles:

Probability of picking a black marble after picking a red marble = Number of black marbles / Total number of remaining marbles
Probability of picking a black marble after picking a red marble = 7 / 24

The overall probability of picking a red marble followed by a black marble is the product of the individual probabilities:

Probability of picking a red then a black marble = Probability of picking a red marble first * Probability of picking a black marble after picking a red marble
Probability of picking a red then a black marble = (12/25) * (7/24)