MATH 10 – WORKSHEET -- TEST ON CHAPTERS 4 AND 5             Merced College;  Don Power  

 

1.  A luncheon special includes one of ___ different soups, one of ___ different types of meat and one of ___ different types of bread, along with ___ side dishes chosen from a group of ___.  How many different luncheon special choices are possible?

 

2.  The following table specifies the probabilities that Al’s Towing Service will receive 0, 1, 2, 3, 4, or 5 calls for help during the evening rush hour.  What is the expected number of calls that Al’s Towing will receive during the evening rush hour?

 

Number of calls

0

1

2

3

4

5

 

Probability

____

___

___

___

___

____

 

3.  If a district attorney feels that the odds are ___ to ___ that she will win her case, what is her personal probability that she will win the case?

 

4.  A carton of ___ light bulbs contains ___ that are defective.  If ___ light bulbs are chosen at random, what is the probability that exactly ___ of them will be defective?

 

5.  If region A represents the event that a

student is studying ____ and region B

represents the event that a student is studying

_____, describe in words what is represented

by the region numbered:

      a.  Number ___.

      b.  Number ___.

 

6.  Given that P(A) = ___ and P(B) = ___ and P(AÇB) = ___,[or P(AÈB) = ___]

      a.  Find P(AÈB). [or P(AÇB)]

      b.  Calculate P(A|B). [or P(B|A)

      c.  Determine whether or not A and B are independent events.  (Show why you chose your answer.)

 

7.  This chart shows the sums that result when two ordinary dice are rolled.  Let x be the sum of the spots on the two dice.  Based on the chart, find P(x ³ ___).[or P(x< ___)]

 

 

1

2

3

4

5

6

 

1

2

3

4

5

6

7

 

2

3

4

5

6

7

8

 

3

4

5

6

7

8

9

 

4

5

6

7

8

9

10

 

5

6

7

8

9

10

11

 

6

7

8

9

10

11

12

 

8.  How many ways are there of choosing ___ people from among __ people to receive door prizes at a party, if the prizes are all the same?  Show at least one formula and the resulting number.

 

9.  How many ways are there to choose ___ people from among ___ people to receive different prizes: a first prize, a second prize,  etc.?  Show at least one formula and the resulting number.

 

10.  Write out ___ rows of Pascal’s Triangle.  Highlight or circle the entry for

 

11.  Simplify the expression  without using a calculator.  Show your work.

 

12.  All the numbers from ___ to ___ are placed in a hat and five numbers are drawn at random.  The numbers are then put back into the hat and the experiment is repeated.  The results are

A = {__, __, __, ___, ___} and B = {__, __, __, __, __}.

List the elements of the following sets:

      a. AÈB

      b. A¢                             or similar sets and set combinations.

      c. A¢ÈB

      d. AÇB¢

 

13.  A survey of ___ high school seniors (___ boys and __ girls) showed that ___ of them like pizza (__ boys and __ girls) but only __ like spinach (__ boys and __ girls).  Let B, G, P and S be the events that a person is a boy, a girl, likes pizza and likes spinach, respectively.

      a.  Determine the probability P(S½G).  [or a similar probability]

      b.  State in words what probability is expressed by P(P½B). [or a similar probability]

 

14.  In a review of patients treated for a rare disease, it is found that __% recovered and __% did not.  Of those who recovered, the review board determines that __% had received the correct treatment.  Of those who did not recover, only __% had received the correct treatment.  Find the probability that a patient who received the correct treatment would recover from the disease.

 

 

 

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