Question

section 5.1 homework score: 6/17 answered: 6/17 question 7 a bowl contains 11 marbles that consist of 6 red, 4 white, and 1 black marbles. one marble is selected at 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: Recall probability formula

The probability of an event $E$ is $P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$.

Step2: Calculate total number of outcomes

The total number of marbles is $6 + 4+1=11$. So the total number of outcomes when selecting a marble is $n = 11$.

Step3: Calculate number of white - marble outcomes

The number of white marbles is $m = 4$.

Step4: Calculate $P(\text{White})$

Using the probability formula $P(\text{White})=\frac{4}{11}$.

For the question "Is each outcome equally likely?":
The outcomes are not equally likely because the number of red marbles ($6$), white marbles ($4$) and black marbles ($1$) are different. The probability of getting a red marble is $P(\text{Red})=\frac{6}{11}$, the probability of getting a white marble is $P(\text{White})=\frac{4}{11}$ and the probability of getting a black marble is $P(\text{Black})=\frac{1}{11}$.

For the question "Which outcome is more likely?":
The red outcome is more likely since $P(\text{Red})=\frac{6}{11}$, $P(\text{White})=\frac{4}{11}$ and $P(\text{Black})=\frac{1}{11}$, and $\frac{6}{11}>\frac{4}{11}>\frac{1}{11}$.

Answer:

Is each outcome equally likely? No
Which outcome is more likely? Red
$P(\text{White})=\frac{4}{11}$