Question

a spinner contains four sections: red, blue, green, and yellow. joaquin spins the spinner twice. the set of outcomes is given as ( s={rb,rg,ry,rr,br,bg,by,bb,gr,gb,gy,gg,yr,yb,yg,yy} ). if the random variable is yellow (y), which of the following is the correct probability distribution? yellow: ( x ) probability: ( p_x(x) ) 0 0.5625 1 0.375 2 0.0625 yellow: ( x ) probability: ( p_x(x) ) 0 0.75 1 0.25 2 0 yellow: ( x ) probability: ( p_x(x) ) 0 0.5 1 0.375 2 0.125 yellow: ( x ) probability: ( p_x(x) )

Explanation:

Step1: Count total number of outcomes

The set \( S \) has \( n(S)=16\) outcomes.

Step2: Calculate \( P(X = 0)\)

Number of outcomes with \( 0\) yellows: \(9\) (RR, RB, RG, BR, BB, BG, GR, GB, GG). So \(P(X = 0)=\frac{9}{16}=0.5625\)

Step3: Calculate \( P(X = 1)\)

Number of outcomes with \(1\) yellow: \(6\) (RY, BY, GR, YR, YB, YG). So \(P(X = 1)=\frac{6}{16}=0.375\)

Step4: Calculate \( P(X = 2)\)

Number of outcomes with \(2\) yellows: \(1\) (YY). So \(P(X = 2)=\frac{1}{16}=0.0625\)

Answer:

The first probability distribution (with \(P(X = 0)=0.5625\), \(P(X = 1)=0.375\), \(P(X = 2)=0.0625\)) is correct.