T102 Multistage Experiments

Use probability tree as needed to solve each problem.

 

1.  A container contains 7 red marbles, 5 blue marbles, and 3 white marbles.

a)  If one marble is drawn at random from the container, find the probability that it is red.

            b)  If two marbles are drawn, one at a time, without replacement, find the probability that they are both the same color.

            c)  If two marbles are drawn, one at a time, with replacement, find the probability that they are both the same color.

 

2.  A box contains three blue cards and four white cards.  If two cards are drawn one at a time, find the probability that both cards are blue if the draws are made as follows:

            a)  with replacement

            b)  without replacement

 

3.  The probability of Ann passing her math test is 80%.  The probability the she passes her English test is 90%.  The probability she passes her Chemistry test is 75%.  What is the probability that she passes all 3 tests?

 

4.  On a certain street there are three traffic lights.  At any given time, the probability that a light is green is 0.3.  What is the probability that a person will hit all three lights when they are green?

 

5.  If a letter is drawn from container 1, shown below and placed in container 2, and then a letter is drawn from container 2, what is the probability that the last letter drawn is an E?

         

CARE

 

CHEER

#1

 

#2

 

6.  You come home on a dark night and find the porchlight burned out.  Since you cannot tell which key is which, you randomly try the five keys on your key ring until you find one that opens your apartment door.  Two of the keys on your key ring unlock the door.        

            a)  Determine the probability of opening the door on the first or second try.

            b)  Determine the probability that it took three or more tries to open the door.

 

7.  If a couple plans to have 3 children, what is the probability of having at least 2 boys?

 

8.  For the containers below, select a container at random, and then select a letter from the chosen container.  What is the probability that the letter chosen is an A?

FALL

 

DAY

#1

 

#2

 

 

 

Solutions

 

1.  a)  7/15        b)  RR + BB + WW = 

c) 

2.  With:           Without: 

3.  .8 X .9 X .75 = .54

4.  .3 X .3 X .3 = .027

5.  Prob – not E from first and E from second OR E from first and E from second.

6.  a)  P(First) + P(Second) =

     b)    or   Complement of answer a)   1 – (Prob first or second) =

7.  .5

8.  Prob (#1 and A) + P(#2 and A) =