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|

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 $P(X = 2)=\frac{1}{4}=0.25$.