A bag contains 4 blue marbles, 10 green marbles, and 11 yellow marbles. You draw a marble, put it back in the bag, and then draw a marble again. Find P(yellow, then blue).
11/25 * 4/25 = ?
To find the probability of drawing a yellow marble first, followed by a blue marble, we need to calculate the individual probabilities and then multiply them together.
Step 1: Calculating the probability of drawing a yellow marble first:
Total number of marbles = 4 (blue) + 10 (green) + 11 (yellow) = 25
Probability of drawing a yellow marble = Number of yellow marbles / Total number of marbles = 11 / 25 = 0.44
After putting the marble back in the bag, the total number of marbles remains the same.
Step 2: Calculating the probability of drawing a blue marble second:
Probability of drawing a blue marble = Number of blue marbles / Total number of marbles = 4 / 25 = 0.16
Step 3: Calculating the probability of both events occurring:
Probability of drawing a yellow marble, then a blue marble = Probability of drawing a yellow marble first * Probability of drawing a blue marble second
P(yellow, then blue) = 0.44 * 0.16 = 0.0704
So, the probability of drawing a yellow marble first, followed by a blue marble is 0.0704 or 7.04%.
To find the probability of drawing a yellow marble and then a blue marble, we need to calculate two probabilities: the probability of drawing a yellow marble on the first draw and the probability of drawing a blue marble on the second draw, given that a yellow marble was already drawn.
1. Probability of drawing a yellow marble on the first draw:
There are a total of 4 + 10 + 11 = 25 marbles in the bag, and 11 of them are yellow. Therefore, the probability of drawing a yellow marble on the first draw is P(Yellow) = 11/25.
2. Probability of drawing a blue marble on the second draw, given that a yellow marble was already drawn:
Since we put the marble back in the bag after each draw, the number of marbles in the bag remains the same for the second draw. Now, we have 25 marbles in the bag, but only 4 of them are blue since we drew a yellow marble first. Therefore, the probability of drawing a blue marble on the second draw, given that a yellow marble was already drawn, is P(Blue|Yellow) = 4/25.
To find P(yellow, then blue), we multiply these probabilities together:
P(yellow, then blue) = P(Yellow) x P(Blue|Yellow)
= (11/25) x (4/25)
= 44/625
Thus, the probability of drawing a yellow marble and then a blue marble is 44/625.