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 outcomes

The set of outcomes $S$ has $n(S)=16$ elements.

Step2: Calculate probability of $X = 0$ (no yellow)

The outcomes with no yellow are $\{RB, RG, RR, BR, BG, BB, GR, GB, GG\}$, so $n(X = 0)=9$. Then $P(X = 0)=\frac{9}{16}=0.5625$.

Step3: Calculate probability of $X = 1$ (one yellow)

The outcomes with one - yellow are $\{RY, BY, YR, YB, GY, YG\}$, so $n(X = 1)=6$. Then $P(X = 1)=\frac{6}{16}=0.375$.

Step4: Calculate probability of $X = 2$ (two yellows)

The outcome with two yellows is $\{YY\}$, so $n(X = 2)=1$. Then $P(X = 2)=\frac{1}{16}=0.0625$.

Answer:

The first probability - distribution table (where $P(X = 0)=0.5625$, $P(X = 1)=0.375$, $P(X = 2)=0.0625$) is the correct one.