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

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}

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

→Probability Distribution of , x

$[x=0,1,2].[P(X)=(\frac{1}{4},\frac{1}{2},\frac{1}{4})]$

Answer 2

It would land on blue maybe one out of two times