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, ( p_x(x) )?

Explanation:

Step1: Calculate probability for \(X = 0\)

When \(X = 0\) (no blue, i.e., \(RR\)), number of favorable outcomes \(n = 1\). Total outcomes \(N=4\). Probability \(P(X = 0)=\frac{1}{4}=0.25\)

Step2: Calculate probability for \(X = 1\)

When \(X = 1\) (either \(RB\) or \(BR\)), number of favorable outcomes \(n = 2\). Probability \(P(X = 1)=\frac{2}{4}=0.5\)

Step3: Calculate probability for \(X = 2\)

When \(X = 2\) (i.e., \(BB\)), number of favorable outcomes \(n = 1\). Probability \(P(X = 2)=\frac{1}{4}=0.25\)

Answer:

The first table (with \(P_X(0) = 0.25\), \(P_X(1)=0.5\), \(P_X(2) = 0.25\)) is the correct probability distribution.