Question

A container holds 9 red markers, 13 blue markers, and 17 green markers. You will randomly select two markers without replacement.
a.) Fill in the probabilities on each branch of the tree diagram. Use the boxes with the fraction bars already provided.

b.) Use the tree diagram to answer the following:

• How many ways can you select the markers?

• How many ways can you select exactly 1 blue marker?

• What is the probability that you select 2 red markers?

• What is the probability that you select a green marker and then a red marker?

Answer 1

Answer:

a.

                         R-------8/38--------RR

R------9/39--------B-------13/38-------RB

                          G------17/38--------RG

                          R-------9/38--------BR

B--------13/39------B-------12/38-------BB

                           G-------17/38-------BG

                             R-----9/38--------GR

G---------17/39-------B------13/38-------GB

                              G------16/38-------GG

b).

• 9 ways
• ways you can select 1 blue are; RB,BR,BG,GB

RB=9/39 × 13/38=3/38

BR= 13/39 × 9/38 =3/38

BG= 13/39 × 17/38=17/114

GB= 17/39 × 13/38=17/114

=3/38 +3/38+17/114+ 17/114 =26/57

• Probability of selecting 2 red markers= RR = 9/39 × 8/38 =12/247

• Probability of selecting a green marker and then a red marker= GR= 17/39×9/38 =51/494