Final answer:
The probabilities for drawing marbles of specific colors are calculated based on the total number of marbles and the specific conditions of replacement and non-replacement. The probability of drawing a white marble is 8/27, the probability of drawing a red and then a blue marble with replacement is (5/27) * (14/27), and the probability of drawing a red, a white, and then a blue marble without replacement is (5/27) * (8/26) * (14/25).
Step-by-step explanation:
Probability of Drawing Marbles
Let's solve each part of the question one by one:
a) Probability of drawing a white marble:
There are 5 red, 8 white, and 14 blue marbles. The total number of marbles is 5 + 8 + 14 = 27. The probability of drawing one white marble is the number of white marbles divided by the total number of marbles, which is 8/27.
b) Probability of drawing a red marble and then a blue marble, with replacement:
The probability of drawing a red marble is 5/27. Since we're replacing the marble, the probability of then drawing a blue marble remains the same: 14/27. Thus, the combined probability is the product of the two probabilities: (5/27) * (14/27).
c) Probability of drawing a red, a white, and then a blue marble, without replacement:
The probability of drawing a red marble first is 5/27. After drawing a red marble, there are 26 marbles left. The probability of drawing a white marble now is 8/26. After that, there are 25 marbles left, and the probability of drawing a blue marble is 14/25. The combined probability is the product: (5/27) * (8/26) * (14/25).