Question

alonso has a bag of marbles with 4 blue marbles, 3 white marbles, and 4 red marbles. find the following probabilities of alonso drawing the given marbles from the bag if the marbles are selected one a time without replacement. (give your answer as a fraction or a decimal rounded to 4 places.) 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 marbles

Total marbles = 4 (blue) + 3 (white) + 4 (red) = 11.

Step2: Calculate probability of a)

Probability of blue first: $\frac{4}{11}$. After drawing a blue, there are 10 marbles left. Probability of red next: $\frac{4}{10}$. So probability of blue then red is $\frac{4}{11}×\frac{4}{10}=\frac{16}{110}=\frac{8}{55}\approx0.1455$.

Step3: Calculate probability of b)

Probability of red first: $\frac{4}{11}$. After drawing a red, there are 10 marbles left. Probability of white next: $\frac{3}{10}$. So probability of red then white is $\frac{4}{11}×\frac{3}{10}=\frac{12}{110}=\frac{6}{55}\approx0.1091$.

Step4: Calculate probability of c)

Probability of first blue: $\frac{4}{11}$. After drawing one blue, there are 10 marbles left. Probability of second blue: $\frac{3}{10}$. After drawing two blues, there are 9 marbles left. Probability of third blue: $\frac{2}{9}$. So probability of three - blues is $\frac{4}{11}×\frac{3}{10}×\frac{2}{9}=\frac{24}{990}=\frac{4}{165}\approx0.0242$.

Answer:

a) $\frac{8}{55}\approx0.1455$
b) $\frac{6}{55}\approx0.1091$
c) $\frac{4}{165}\approx0.0242$