martina has a bag of marbles with 2 blue marbles, 4 white marbles, and 3 red marbles. find the following…

martina has a bag of marbles with 2 blue marbles, 4 white marbles, and 3 red marbles. find the following probabilities of martina 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 =

martina has a bag of marbles with 2 blue marbles, 4 white marbles, and 3 red marbles. find the following probabilities of martina 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 =

Answer

Explanation:

Step1: Calculate total number of marbles

Total marbles = 2 (blue) + 4 (white) + 3 (red) = 9

Step2: Calculate probability for part a

Probability of drawing a blue first is $\frac{2}{9}$, and since it's with - replacement, probability of drawing a red second is $\frac{3}{9}$. The combined probability is $\frac{2}{9}\times\frac{3}{9}=\frac{6}{81}\approx0.074$

Step3: Calculate probability for part b

Probability of drawing a red first is $\frac{3}{9}$, and probability of drawing a white second (with - replacement) is $\frac{4}{9}$. The combined probability is $\frac{3}{9}\times\frac{4}{9}=\frac{12}{81}\approx0.148$

Step4: Calculate probability for part c

Probability of drawing a blue each time (with - replacement) is $\frac{2}{9}$. So the probability of drawing blue three times is $\left(\frac{2}{9}\right)^3=\frac{8}{729}\approx0.011$

Answer:

a) 0.074 b) 0.148 c) 0.011