Question

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, PX(x)?

Answer 1

It is Graph A

Explanation:

Answer 2

Answer with explanation:

Number of Sections in which Spinner is divided = Red +Blue

Set of possible outcomes when the spinner is spun twice is S = {RR, RB, BR, BB}

x=Number of times blue Occurs

={0,1,2}

→→Probability Distribution of , x

x=0, blue has Occurred none out of 4 possible Outcomes when the spinner is spun twice.={BB}

x=1, blue has Occurred once out of 4 possible Outcomes when the spinner is spun twice.={RB,BR}

x=2, blue has Occurred twice out of 4 possible Outcomes when the spinner is spun twice.={RR}

`P(X)_(x=0)=\frac{\text{Total favorable outcome}}{\text{Total favorable outcome}}\\\\=(BB)/((RR+ RB+ BR+ BB))\\\\=(1)/(4)\\\\P(X)_(x=1)=(RB+BR)/((RR+ RB+ BR+ BB))\\\\P(X)_(x=1)=(2)/(4)\\\\P(X)_(x=1)=(1)/(2)\\\\P(X)_(x=2)=(RR)/((RR+ RB+ BR+ BB))\\\\P(X)_(x=2)=(1)/(4)`

→Probability Distribution of , x

`[x=0,1,2].[P(X)=((1)/(4),(1)/(2),(1)/(4))]`