A bag contains 5 red, 5 blue, 5 green, and 5 white marbles. Two marbles are drawn, but the first marble is not replaced. Find P(red, then blue)
To find the probability of drawing a red marble, then a blue marble without replacement, we need to find two probabilities: the probability of drawing a red marble first (without replacement), and the probability of drawing a blue marble second (given that the first marble drawn was red).
Step 1: Find the probability of drawing a red marble first:
There are a total of 20 marbles in the bag, and 5 of them are red. So the probability of drawing a red marble on the first draw is 5/20 or 1/4.
Step 2: Find the probability of drawing a blue marble second (given that the first marble drawn was red):
After the first marble is drawn, there are 19 marbles left in the bag, and 5 of them are blue. So the probability of drawing a blue marble on the second draw is 5/19.
Step 3: Multiply the probabilities of the two events:
To find the probability of both events happening, we multiply the probabilities. Therefore, the probability of drawing a red marble, then a blue marble is (1/4) * (5/19).
Calculating this expression, we get:
(1/4) * (5/19) = 5/76
So the probability of drawing a red marble, then a blue marble from the bag without replacement is 5/76.