edgar has a bag of marbles with 5 blue marbles, 2 white marbles, and 2 red marbles. find the following…

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.\na) a blue, then a red =\nb) a red, then a white =\nc) a blue, then a blue, then a blue =

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.\na) a blue, then a red =\nb) a red, then a white =\nc) a blue, then a blue, then a blue =

Answer

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) $0.172$