a spinner is divided into two equal parts, one red and one blue. the set of possible outcomes when the…

a spinner is divided into two equal parts, one red and one blue. the set of possible outcomes when the spinner is spun twice is s = {rr, rb, br, bb}. let x represent the number of times blue occurs. which of the following is the probability distribution, $p_x(x)$?\n|x|px(x)|\n|0|0.25|\n|1|0.5|\n|2|0.25|\n|x|px(x)|\n|0|0.33|\n|1|0.33|\n|2|0.33|\n|x|px(x)|\n|0|0.5|\n|1|0.5|\n|2|0|\n|x|px(x)|\n|0|0|\n|1|0.5|
Answer
Answer:
A.
| X | $P_X(x)$ |
|---|---|
| 0 | 0.25 |
| 1 | 0.5 |
| 2 | 0.25 |
Explanation:
Step1: Calculate total outcomes
There are 4 total outcomes: ${RR, RB, BR, BB}$.
Step2: Find $P(X = 0)$
No blue occurs only when outcome is $RR$. So $P(X = 0)=\frac{1}{4}= 0.25$.
Step3: Find $P(X = 1)$
One - blue occurs for $RB$ and $BR$. So $P(X = 1)=\frac{2}{4}=0.5$.
Step4: Find $P(X = 2)$
Two - blues occur when outcome is $BB$. So $P(X = 2)=\frac{1}{4}=0.25$.