Question

edgar has a bag of marbles with 5 blue marbles, 2 white marbles, and 2 red marbles. find the following probabilities of edgar drawing the given marbles from the bag if the drawings are done with replacement. round answers to three decimal places when appropriate.
a) a blue, then a red =
b) a red, then a white =
c) a blue, then a blue, then a blue =

Explanation:

Step1: Calculate total number of marbles

The total number of marbles is $5 + 2+2=9$.

Step2: Calculate probability of a blue - then a red

The probability of drawing a blue marble first is $\frac{5}{9}$, and since the drawing is with replacement, the probability of drawing a red marble second is $\frac{2}{9}$. The combined probability is $\frac{5}{9}\times\frac{2}{9}=\frac{10}{81}\approx0.123$.

Step3: Calculate probability of a red - then a white

The probability of drawing a red marble first is $\frac{2}{9}$, and the probability of drawing a white marble second is $\frac{2}{9}$. The combined probability is $\frac{2}{9}\times\frac{2}{9}=\frac{4}{81}\approx0.049$.

Step4: Calculate probability of three blue marbles

The probability of drawing a blue marble each time (since with replacement) is $\frac{5}{9}\times\frac{5}{9}\times\frac{5}{9}=\frac{125}{729}\approx0.172$.

Answer:

a) $0.123$
b) $0.049$
c) $0.172$