Question

"Make a tree diagram to determine the theoretical probability for this experiment: Spin the arrows (not shown) on each of the following three spinners, and note the color where the arrow lands on each spinner. Spinner 1 is divided into two equal sectors, labeled “Red” and “Blue.” Spinner 2 is first divided into two equal sectors. The left is labeled “Green.” The right is then divided into two equal sectors, labeled “Red” and “Blue.” Spinner 3 is divided into three equal sectors, labeled “Red,” “Blue,” and “Green.” Give the sample space for the experiment and the probability of each outcome. What is the probability of getting at least 1 red? What is the probability of getting at least 1 blue?"

Answer 1

Tree diagram to determine the theoretical probability for the experiment: Spin the arrows is given in following figure.

The Sample space for this experiment is given by:

S={RGR,RGB,RGG,RRR,RRB,RRG,RBR,RBR,RBG,BGR,BGB,BGG,BRR,BRB,BRG,BBR,BBB,BBG}

n(S)=18

Let P be the event of getting at least 1 Red.

P={RGR,RGB,RGG,RRR,RRB,RRG,RBR,RBR,RBG,BGR,BRR,BRB,BRG,BBR}

n(P)=14

The probability of getting at least 1 red is given by:

Let Q be the event of getting at least 1 blue.

Q={RGB,RRB,RBR,RBR,RBG,BGR,BGB,BGG,BRR,BRB,BRG,BBR,BBB,BBG}

n(Q)=14