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Probability and rate

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Newbie | Next Rank: 10 Posts
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by eririn » Wed Nov 28, 2007 5:34 pm
:)
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 incluede the spoiled apple?

A. 1/5
B. 3/10
C. 2/5
D. 1/2
E. 3/5

Ans. C

:(
Suzan drove at an average speed of 30 miles per hour for the first 30 miles of a trip and then at an average speed of 60 miles per hour for the remaining 30 miles of the trip. If she made no stops during the trip, what was Susan's average speed, in miles per hour, for the entire trip?

A. 35
B. 40
C. 45
D. 50
E. 55

Ans. B
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by syv11 » Wed Nov 28, 2007 6:54 pm
Question 1:

Probability of bad apple: 1/5. Simultaneously: 1/5+1/5=2/5

Question 2:

Suzan drove at an average speed of 30 miles per hour for the first 30 miles of a trip and then at an average speed of 60 miles per hour for the remaining 30 miles of the trip. If she made no stops during the trip, what was Susan's average speed, in miles per hour, for the entire trip?

first 30 miles at 30mph ===> 1h
second 30 miles at 60mph ===> 30m/60mph==>0.5h

Total distance 60 miles
time 1.h
average speed 40mph
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by camitava » Wed Nov 28, 2007 11:19 pm
For second Qs, I agree with the approach which syv11 has taken.
But for 1, I am having some different approach - u can say -
We can take 2 apples out of 5 in 5C2 = 10 ways
Now 1 of the selected apple should be rotten and it can chosen in only 1 way.
The rest one apple can be chosen in = (5 - 1) = 4 ways
So total favorable oppurtunity = 4 + 1 = 5
So probability = 5 / 10 = 1/2. So IMO - D.
Now guys I am getting confused where I am wrong? But I can ask syv11 (Pls dnt mind) when u r taking 1/5 for the good apple - it will also the rotten apple also. Guys more input reqd. here.
Correct me If I am wrong


Regards,

Amitava
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by projase » Thu Nov 29, 2007 7:35 am
camitava wrote:For second Qs, I agree with the approach which syv11 has taken.
But for 1, I am having some different approach - u can say -
We can take 2 apples out of 5 in 5C2 = 10 ways
Now 1 of the selected apple should be rotten and it can chosen in only 1 way.
The rest one apple can be chosen in = (5 - 1) = 4 ways
So total favorable oppurtunity = 4 + 1 = 5
So probability = 5 / 10 = 1/2. So IMO - D.
Now guys I am getting confused where I am wrong? But I can ask syv11 (Pls dnt mind) when u r taking 1/5 for the good apple - it will also the rotten apple also. Guys more input reqd. here.
For me the easiest way to solve this is the following:

You can choose the bad apple either the first time or the sencond time.
The probailities to choose the bad the first time are 1/5.
The probailities to choose it the second time are = No First and Yes Second = 4/5 x 1/4 = 1/5.
So 1/5+1/5 = 2/5
Where there's a will, there's a way...
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