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, PX(x)?

Answer 1

The person above is correct!

The answer is A)

Answer 2

Suppose that the spinner is spun twice. Find the probabilities:

`Pr(X=0),\ Pr(X=1),\ Pr(X=2).`

1. When X=0, blue occurs 0 times. There is one favorable outcome (RR) from four possible. Then

`Pr(X=0)=(1)/(4).`

2. When X=1, blue occurs 1 times. There are two favorable outcomes (RB and BR) from four possible. Then

`Pr(X=1)=(2)/(4)=(1)/(2).`

3. When X=2, blue occurs 2 times. There is one favorable outcome (BB) from four possible. Then

`Pr(X=2)=(1)/(4).`

At last, the distribution table takes look

`\begin{array}{cccc}x_i &|\ 0 & 1 & 2 \\------& -- &---&--- \\Pr(X=x_i) & \left |\ (1)/(4) & (1)/(2) & (1)/(4)\end{array}`