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Commonly Used Formulas in Probability Odds P(A)1 P(A) General…

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Commonly Used Formulas in Probability Odds:P(A)1...
Commonly Used Formulas in Probability
Odds:P(A)1 - P(A)
General Law of Addition: P(A ? B) = P(A) + P(B) - P(A n B)
Conditional probability: P(A | B) = P(A n B)P(B)
Independence property: P(A n B) = P(A)P(B)
Bayes’s Theorem: P(B | A) = P(A | B)P(B)
P(A | B)P(B) + P(A | B_)P(B_)
Permutation: n Pr = n!(n - r )!
Combination: nCr = n!r !(n - r )!
5.62 A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a 1-hour flight is .02. What is the probability that (a) both will fail? (b) Neither will fail? (c) One or the other will fail? Show all steps carefully.
5.70 The probability is 1 in 4,000,000 that a single auto trip in the United States will result in a fatality. Over a lifetime, an average U.S. driver takes 50,000 trips. (a) What is the probability of a fatal accident over a lifetime? Explain your reasoning carefully. Hint: Assume independent events. Why might the assumption of independence be violated? (b) Why might a driver be tempted not to use a seat belt “just on this trip”?
Submitted: 8 years ago.Category: Math Homework
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Answered in 1 hour by:
6/15/2010
Math Tutor or Teacher: chindhu,
 replied 8 years ago
chindhu
Category: Math Homework
Satisfied Customers: 798
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Hi,

Click here for the answer.

When you click on the above link, it will lead to www.mediafire.com.There you can see that "Click here to start download", Click on that you will get your answer as a word file.
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Math Tutor or Teacher: Scott, MIT Graduate replied 8 years ago
Scott
Scott, MIT Graduate
Category: Math Homework
Satisfied Customers: 17,710
Experience: Over 13,000 accepts & 100% feedback in the old math category
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Hi there,

 

The answer to the driving question that he posted is wrong, math-wise. Think about what would happen using that formula with over 4,000,000 trips -- the probability would be greater than 1, which is impossible.


Here is the actual solution:

prob(no accident) =(NNN) NNN-NNNN4000000

prob(no accident for 50000 trips) = (3999999/4000000)^50000
prob(accident for 50000 trips) = 1 - previous result
= 1 - (3999999/4000000)^50000
= about 0.012422

 

In addition, I think the last part of the first question implies that one OR the other fails, NOT both... so the answer is actually 1 - 0.0004 - 0.9604 = 0.0392

 

Let me know if you have any questions,
Scott



Edited by Scott on 6/15/2010 at 3:28 AM EST
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Math Tutor or Teacher: chindhu,
 replied 8 years ago
Hi,

The probability of single trip that results in a fatality is 1/4,000,000.
that is obviously less than 1. It happens 50000 times. So we can multiply 1/4000,000 with 50,000 to get the probability of a fatal accident over a lifetime.

How you can say that 1/4,000,000*50,000 = 0.0125 is greater than 1.
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Math Tutor or Teacher: Scott, MIT Graduate replied 8 years ago

Hey,

 

Sorry for any confusion about this answer. The other person's method is clearly incorrect. Imagine that they took 5,000,000 trips. By his reasoning, the probability of getting into an accident would be:

1/4000000 *(NNN) NNN-NNNN/p>

= 1.25

 

One of the very first things you learn when studying probabilty is that probability values CANNOT be greater than 1 under any circumstance.

 

That proves that his answer is wrong, and his reasoning is wrong.

 

The correct (and only) answer is:

prob(no accident) =(NNN) NNN-NNNN4000000

prob(no accident for 50000 trips) = (3999999/4000000)^50000
prob(accident for 50000 trips) = 1 - previous result
= 1 - (3999999/4000000)^50000
= about 0.012422

 

Let me know if you have any questions,

-Scott

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Math Tutor or Teacher: chindhu,
 replied 8 years ago

Hello expert Scott,

 

1/4000000 * 50,000 =50,000/4,000,000

= .0125 (answer is 0.0125)

 

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Math Tutor or Teacher: Scott, MIT Graduate replied 8 years ago

Hey,

 

Dulan, I'm truly sorry the other person keeps posting the same incorrect answer, even though it's quite clear that it's wrong... Again, the answer is NOT 0.0125. Please do NOT hand that in, since it will be marked incorrect by your teacher, for lack of knowledge of the correct methods of probability.

 

The way that he can see that it's wrong is to pretend that your question asked about taking 5,000,000 trips. By his reasoning, the probability of getting into an accident would be:

1/4000000 *(NNN) NNN-NNNN/p>

= 1.25

 

Think about 10,000,000 trips! By his method, it would be:

1/4000000 * 10000000

= 2.5

That means you are not only guaranteed to die if you take that many trips, but die 2 and a half times! LOL!

 

One of the very first things you learn when studying probabilty is that probability values CANNOT be greater than 1 under any circumstance. If you see a method that can give a p > 1 (like his, as is clear from my two examples above), then you know you did something wrong.

 

That proves that his answer is wrong, and his reasoning is wrong.

 

Again, the correct (and only) answer is:

prob(no accident) =(NNN) NNN-NNNN4000000

prob(no accident for 50000 trips) = (3999999/4000000)^50000
prob(accident for 50000 trips) = 1 - previous result
= 1 - (3999999/4000000)^50000
= about 0.012422

 

Here are a couple similar posts from other experts who clearly have the same answer as me:

http://www.justanswer.com/questions/2usyy-question-1-a-certain-airplane-has-two-independent-alternators

http://www.justanswer.com/questions/3kq23-the-probability-is-1-in-4-000-000-that-a-single-auto-trip-in

 

Let me know if you have any questions, and again, I'm really sorry that he keeps posting the wrong information for you. Please do not submit that other answer.

-Scott



Edited by Scott on 6/15/2010 at 4:03 AM EST
Scott
Scott, MIT Graduate
Category: Math Homework
Satisfied Customers: 17,710
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Scott and 87 other Math Homework Specialists are ready to help you
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Math Tutor or Teacher: chindhu,
 replied 8 years ago
Hi Dulan and expert Scott,

Sorry for the trouble.... Understood my mistake.....
Sorry once again.....
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