Question

section 5.1 homework
score: 6/17 answered: 6/17
question 7
a bowl contains 14 marbles that consist of 4 red, 2 white, and 8 black marbles. one marble is select random from the bowl and the color is observed.
the possible outcomes are {red, white, black}
is each outcome equally likely?
which outcome is more likely? select an answer
p(white) = give answer as a fraction.

Explanation:

Step1: Calculate total number of marbles

There are 14 marbles in total.

Step2: Calculate probability of each color

The probability of an event $E$ is given by $P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$.
For red marbles: $P(\text{Red})=\frac{4}{14}=\frac{2}{7}$.
For white marbles: $P(\text{White})=\frac{2}{14}=\frac{1}{7}$.
For black marbles: $P(\text{Black})=\frac{8}{14}=\frac{4}{7}$.

Step3: Check equal - likelihood

Since $\frac{2}{7}
eq\frac{1}{7}
eq\frac{4}{7}$, the outcomes are not equally likely.

Step4: Determine the most likely outcome

Since $\frac{4}{7}>\frac{2}{7}>\frac{1}{7}$, black is the more likely outcome.

Answer:

No, black, $\frac{1}{7}$