hi

please see 8 questions attached below.please solve showing the work.

thanks

3

Homework 1.1

• True or False?

C)BA(CBA

A)BA(A

)CB(AC)BA(

)CB(AC)BA(

BABA

4

Homework 1.2

Juan is playing the following game: he rolls two dice. If they sum up

to 7 he loses a dollar. If they sum up to 2, he wins 2 dollars.

Otherwise, he doesn’t win nor lose.

After playing this game for a long time, what shall happen? why?

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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.

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?

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Homework 1.4

Harold and Mary 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”?

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Homework 1.5

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?

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Homework 1.6

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?

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Homework 1.7

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?

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Homework 1.8

Example 1:

An company is considering an investment.

The outcomes can be as follows:

Success: 20%

Average: 50%

Failure: 30%

The company decides to hire a specialist. His advice is either YES or NO.

From past experience, the company knows that:

p(YES|success) = 0.9

p(YES|Average) = 0.2

p(YES|Failure) = 0.1

The specialist said YES. What is the probability for success?