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Again Probability prob

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by selango » Wed May 26, 2010 12:01 am
A basket contains 5 apples,of which 1 is spoiled and the rest are good.If henry is to select 2 apples from the basket simultaneously and at random,what is the probability that the 2 apples selected will include the spoiled apple?


a)1/5

b)3/10

c)2/5

d)1/2

e)3/5


any quick approach?
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by thephoenix » Wed May 26, 2010 12:08 am
there are two ways to solve it one is to find the probability of the given case another is find out the probability of opposite case and subtract it from to get the desired prob......the second is always easy
probability of selecting fresh apples=4/5*3/4=3/5
now desired P=1-3/5=2/5
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by selango » Wed May 26, 2010 12:29 am
I tried the prob in this way

Since they are 2 independent events(ie)selecting good and bad apples

P(selecting good apples)=2/5

P(selecting bad apple)=1/5

P(A.B)=2/5.1/5=2/5


Is it correct?
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by liferocks » Wed May 26, 2010 12:36 am
selango wrote:I tried the prob in this way

Since they are 2 independent events(ie)selecting good and bad apples--events are not independent since the apples are selected without replacement

P(selecting good apples)=2/5--this is 4/5..if the first apple is good and 4/4 if second apple is good

P(selecting bad apple)=1/5--this is 1/4 if second apple is bad and 1/5 is first apple is bad

P(A.B)=2/5.1/5=2/5--multiplication result has a typo

but in this way probability is P(the first apple is good and second apple is bad )+P(the first apple is bad and second apple is good)=4/5 * 1/4 +1/5 * 4/4=1/5 + 1/5 =2/5


Is it correct?
some corrections.
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by selango » Wed May 26, 2010 12:40 am
oops my mistake.

Thanks I got it
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by selango » Wed May 26, 2010 12:50 am
Here one doubt.I would like to know when we have to add or multiply the probability?

Two independent events means we need to multiply the probability.right?
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by liferocks » Wed May 26, 2010 1:00 am
selango wrote:
Two independent events means we need to multiply the probability.right?
this is correct.
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by selango » Wed May 26, 2010 1:07 am
Then in which case should we need to add the prob?
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by liferocks » Wed May 26, 2010 1:12 am
selango wrote:Then in which case should we need to add the prob?
we multiply when the events both will happen and add when either will happen but not both.Like the question we discussed here
P(the first apple is good and second apple is bad )+P(the first apple is bad and second apple is good)

take the first one the two events first apple is good and second apple is bad has to happen together but between the events 'the first apple is good and second apple is bad ' and 'the first apple is bad and second apple is good' only one will happen.
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by selango » Wed May 26, 2010 1:22 am
Thanks liferocks.
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by Thouraya » Sat Jun 12, 2010 3:22 am
Liferocks,

Why did we not divide by the total possible cases which is 5C2 here?

After subtracting from 1, when should we divide by the total number of possible cases and when do we not consider the total number of cases?

Also, with regards to 1-(4/5 x 3/4); why is it 4 over FIVE? aren't we assuming that there are 4 good apples, so why is the total 5 rather than 4?

Thank you!
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