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