Brian has a bag that contains 14 red marbles and 12 yellow marbles. He selects a marble at random, and then, without replacing the first one, selects another marble at random.
What is the probability that Brian selects a red marble and then a yellow marble? Round your answer to the nearest percent.
P(red and yellow) ≈ %
26 total marbles, so
P(red,yellow) = 14/26 * 12/25
51%
To find the probability of selecting a red marble first and then a yellow marble, you need to calculate the probability of each event happening individually and then multiply the probabilities together.
Let's start by calculating the probability of selecting a red marble first.
The total number of marbles in the bag is 14 (red) + 12 (yellow) = 26.
So the probability of selecting a red marble first is 14/26.
After selecting a red marble, there are now 13 red marbles and 12 yellow marbles left in the bag. The total number of marbles is reduced to 25.
Next, let's calculate the probability of selecting a yellow marble second.
The probability of selecting a yellow marble second, given that a red marble was selected first, is 12/25.
To find the probability of both events happening, we multiply the probabilities together:
P(red and yellow) = (14/26) * (12/25)
Now, we can perform the calculation:
P(red and yellow) ≈ (14/26) * (12/25) ≈ 0.258 ≈ 25.8%
Therefore, the probability that Brian selects a red marble first and then a yellow marble is approximately 25.8% (rounded to the nearest percent).