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 with replacement. round answers to three decimal places when appropriate. a) a blue, then a red = 0.123 b) a red, then a white = 0.049 c) a blue, then a blue, then a blue = 0.17

Explanation:

Step1: Calculate total number of marbles

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

Step2: Find probability of drawing a blue marble each time

Since the drawings are with replacement, the probability of drawing a blue - marble each time is $P(\text{blue})=\frac{5}{9}$.

Step3: Calculate the probability of drawing three blue marbles

For independent events (drawings with replacement), the probability of multiple events occurring is the product of their individual probabilities. So $P(\text{blue, blue, blue})=\frac{5}{9}\times\frac{5}{9}\times\frac{5}{9}=\frac{125}{729}\approx0.171$.

Answer:

$0.171$