Working with
Tree Diagrams
 Topic Index | Algebra Index | Regents Exam Prep Center

  Answer the following questions pertaining to tree diagrams.

1.

You are at a carnival.  One of the carnival games asks you to pick a door and then pick a curtain behind the door.  There are 3 doors and 4 curtains behind each door.  How many choices are possible for the player?

Choose:

3
 12
 24
36

 

 

2.

The 4 aces are removed from a deck of cards.  A coin is tossed and one of the aces is chosen.  What is the probability of getting heads on the coin and the ace of hearts?  Draw a tree diagram to illustrate the sample space.

 

See Tree Diagram

Choose:

1/2
 1/4
 1/8
1/16

 

 

 

3.

There are 3 trails leading to Camp A from your starting position.  There are 3 trails from Camp A to Camp B.  How many different routes are there from the starting position to Camp B?  Draw a tree diagram to illustrate your answer.

 

See Tree Diagram

Choose:

3
 6
 9
12

 

 

4.

A spinner has 4 equally likely regions numbered 1 to 4.  The arrow is spun twice.  What is the probability that the spinner will land on a 1 on the first spin and on a red region on the second spin?  Draw a tree diagram to represent your answer.

 

See Tree Diagram

Choose:

1/2
 1/4
 1/6
1/8

 

 

 

5.

There are two identical bottles.  One bottle contains 2 green balls and 1 red ball.  The other contains 2 red balls.  A bottle is selected at random and a single ball is drawn.  What is the probability that the ball is red?

            Answer

Choose:
 1/2
1/3
 1/6
 2/3

 


 

6.

Mr. Lamb has three children:  two girls (Sue and Karen) and one boy (David).  After each meal, one child is chosen at random to wash dishes.

a.  If the same child can be chosen for both lunch and dinner, list a sample space of all the possible outcomes of who will wash dishes after lunch and dinner on Saturday.
 

b.  Determine the probability that one boy and one girl will wash dishes after lunch and dinner on Saturday.

Answer