Question

a jar contains 5 red marbles, 5 white marbles, and 6 blue marbles. two marbles are randomly selected from the jar with replacement. find the following probabilities. leave your answer as a reduced fraction.
a. a red marble and then a blue marble is randomly selected.
b. a white marble and then a red marble is randomly selected.

Explanation:

Step1: Calculate total number of marbles

The total number of marbles is $5 + 5+6=16$.

Step2: Calculate probability for part a

The probability of selecting a red marble first is $\frac{5}{16}$ since there are 5 red marbles out of 16. Since we are sampling with replacement, the probability of selecting a blue marble second is $\frac{6}{16}$. By the multiplication - rule for independent events, the probability of a red then a blue is $\frac{5}{16}\times\frac{6}{16}=\frac{30}{256}=\frac{15}{128}$.

Step3: Calculate probability for part b

The probability of selecting a white marble first is $\frac{5}{16}$ as there are 5 white marbles out of 16. The probability of selecting a red marble second (with replacement) is $\frac{5}{16}$. By the multiplication - rule for independent events, the probability of a white then a red is $\frac{5}{16}\times\frac{5}{16}=\frac{25}{256}$.

Answer:

a. $\frac{15}{128}$
b. $\frac{25}{256}$