Question

there are four red marbles, six blue marbles, and 5 marbles that are half - red and half - black. you select a marble randomly. find the probabilities below
a. p(blue marble)
b. p(doesnt contain black)

Explanation:

Step1: Calculate total number of marbles

There are 4 red, 6 blue and 6 black marbles. So the total number of marbles is $4 + 6+6=16$ marbles.

Step2: Calculate probability of blue marble (a)

The probability formula is $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. For a blue marble, the number of favorable outcomes is 6 and total number of outcomes is 16. So $P(\text{blue marble})=\frac{6}{16}=\frac{3}{8}$.

Step3: Calculate probability of not - black (b)

The number of non - black marbles is $4 + 6=10$. Total number of marbles is 16. So $P(\text{doesn't contain black})=\frac{10}{16}=\frac{5}{8}$.

Answer:

a. $\frac{3}{8}$
b. $\frac{5}{8}$