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October 31st, 2011, 08:13 AM   #1
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Probability Question

I have been looking over my class notes and could not find an example of how to do this:

A junk box in your room contains ten old batteries, 5 of which are totally dead. You start picking batteries one at a time and testing them.

Find the probability that the first two you choose are both good.


Also,

Find the probability that at least one of first two works.

Is there an easy way to explain these?

Thank you, as always.

EDIT: Just to keep this on one post, I have one further question (maybe more to come )

A commuter must pass through five traffic lights on her way to work and will have to stop at each one that is red. She estimates the probability model for the number of red lights she hits, as shown below:
x = # of red ____ p(x) = P(X=x)
0 0.02
1 0.21
2 0.53
3 0.1
4 0.1
5 0.04

I have found the number of red lights she expects to hit (2.17).
Now it is asking fir the standard deviation. Is there an easy way of doing this? Thank you!
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October 31st, 2011, 10:23 AM   #2
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Re: Probability Question

Quote:
Originally Posted by jskrzy
I have been looking over my class notes and could not find an example of how to do this:

A junk box in your room contains ten old batteries, 5 of which are totally dead. You start picking batteries one at a time and testing them.

Find the probability that the first two you choose are both good.


Also,

Find the probability that at least one of first two works.

Is there an easy way to explain these?

Thank you, as always.
probability that the first two you choose are both good=probability first good * probability second good=(5/10)*(4/9)=2/9
probability that at least one of first two works=1- probability no good battery=1-(5/10)*(4/9)=7/9
wnvl is offline  
October 31st, 2011, 10:28 AM   #3
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Re: Probability Question

Quote:
Originally Posted by jskrzy
A commuter must pass through five traffic lights on her way to work and will have to stop at each one that is red. She estimates the probability model for the number of red lights she hits, as shown below:
x = # of red ____ p(x) = P(X=x)
0 0.02
1 0.21
2 0.53
3 0.1
4 0.1
5 0.04

I have found the number of red lights she expects to hit (2.17).
Now it is asking fir the standard deviation. Is there an easy way of doing this? Thank you!
Calculate first expected value x^2
x^2 = # of red ____ p(x^2)
0 0.02
1 0.21
4 0.53
9 0.1
16 0.1
25 0.04
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October 31st, 2011, 12:48 PM   #4
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Re: Probability Question

Thank you for the help.

Can you clarify the red light problem though?


I do not understand.
jskrzy is offline  
October 31st, 2011, 02:11 PM   #5
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Re: Probability Question

Quote:
Originally Posted by jskrzy
Thank you for the help.

Can you clarify the red light problem though?


I do not understand.
standard deviation = E(x^2) - E(x)^2

E(x) you have already.
Calcultate now E(x^2) using table I provided.
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