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) )?

( x )	( p_x(x) )
1	0.5
2	0.25

( x )	( p_x(x) )
1	0.33
2	0.33

( x )	( p_x(x) )
1	0.5
2	0

Explanation:

Step1: Determine possible values of \( X \)

The spinner is spun twice, and \( X \) is the number of times blue occurs. So \( X \) can be 0, 1, or 2.

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

\( X = 0 \) means no blue occurs, so the outcome is \( RR \). There are 4 total outcomes (\( S=\{RR, RB, BR, BB\} \)), so \( P(X = 0)=\frac{\text{Number of } RR}{\text{Total outcomes}}=\frac{1}{4} = 0.25 \).

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

\( X = 1 \) means blue occurs once. The outcomes are \( RB \) and \( BR \). So the number of favorable outcomes is 2. Then \( P(X = 1)=\frac{2}{4}=0.5 \).

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

\( X = 2 \) means blue occurs twice, so the outcome is \( BB \). The number of favorable outcomes is 1. Thus \( P(X = 2)=\frac{1}{4}=0.25 \).

Answer:

The first probability distribution table (with \( X = 0 \) having \( P_X(x)=0.25 \), \( X = 1 \) having \( P_X(x)=0.5 \), and \( X = 2 \) having \( P_X(x)=0.25 \))