CS513- Homework 1- Solved

Homework 1.1
Jerry and Susan have a joint bank account.

Jerry goes to the bank 20% of the days.

Susan goes there 30% of the days.

Together they are at the bank 8% of the days.

a.            Susan was at the bank last Monday. What’s the probability that Jerry was there too?

b.           Last Friday, Susan wasn’t at the bank. What’s the probability that Jerry was there?

c.            Last Wednesday at least one of them was at the bank. What is the probability that both of them were there?

 

 Homework 1.2
Harold and Sharon are studying for a test.

Harold’s chances of getting a “B” are 80%. Sharon’s chances of getting a “B” are 90%.

The probability of at least one of them getting a “B” is 91%.

a.            What is the probability that only Harold gets a “B”?

b.           What is the probability that only Sharon gets a “B”?

c.            What is the probability that both won’t get a “B”?

Homework 1.3
Jerry and Susan have a joint bank account.

Jerry goes to the bank 20% of the days.

Susan goes there 30% of the days.

Together they are at the bank 8% of the days.

Are the events “Jerry is at the bank” and “Susan is at the bank” independent?

 

Homework 1.4
You roll 2 dice. 

a.           Are the events “the sum is 6” and “the second die shows 5” independent?

b.           Are the events “the sum is 7” and “the first die shows 5” independent?

 Homework 1.5
An oil company is considering drilling in either TX, AK and

NJ. The company may operate in only one state. There is 60% chance the company will choose TX and 10% chance – NJ.

There is 30% chance of finding oil in TX, 20% - in AK, and 10% - in NJ.

 

1.            What’s the probability of finding oil?

2.            The company decided to drill and found oil. What is the probability that they drilled in TX?

 

 Homework 1.6
 

      The following slide shows the survival status of individual passengers on the Titanic. Use this information to answer the following questions

n    What is the probability that a passenger did not survive?

n    What is the probability that a passenger was staying in the first class?

n    Given that a passenger survived, what is the probability that the passenger was staying in the first class?

n    Are survival and staying in the first class independent?

n    Given that a passenger survived, what is the probability that the passenger was staying in the first class and the passenger was a child?

n    Given that a passenger survived, what is the probability that the passenger was an adult?

n    Given that a passenger survived, are age and staying in the first class independent? 

 

 

Survived
Cabin

 
1st
2nd
3rd
Crew
Sub Total
Adult
          197 
             94 
          151 
          212 
654 
Child
               6 
             24 
             27 
              -   
57 
Sub Total
          203 
          118 
          178 
          212 
711
Age

Not Survived
Cabin

 
1st
2nd
3rd
Crew
Sub Total
Adult
          122 
          167 
          476 
          673 
        1,438 
Child
 
 
             52 
 
              52 
Sub Total
          122 
          167 
          528 
          673 
        1,490 
Age

Total

Cabin

 

Adult
1st
2nd
3rd
Crew
Grand Total
          319 
          261 
          627 
          885 
        2,092 
Child

Grand Total
               6 
             24 
             79 
 
           109 
          325 
          285 
          706 
          885 
        2,201 
Age

 Homework 1.7
Replace the missing values below (?), assuming independence between age and cabin class

Total
Cabin

 

Adult
1st
2nd
3rd
Crew
Grand Total
?
?
?
? 
        2,092 
Child

Grand Total
?
?
?
 ?
           109 
          325 
          285 
          706 
          885 
        2,201 
Age

Replace the missing values below (?), assuming independence between age and cabin class given survival status (conditional independence)

Survived
Cabin

 
1st
2nd
3rd
Crew
Sub Total
Adult
?
?
  ?
 ?
           654 
Child
?
?
?
?
              57 
Sub Total
          203 
          118 
          178 
          212 
711
Age

Not Survived
Cabin

 
1st
2nd
3rd
Crew
Sub Total
Adult
  ? 
?
?
?
        1,438 
Child
 ?
?
?
?
              52 
Sub Total
          122 
          167 
          528 
          673 
        1,490 
Age