Question 33819: There are two boxes A and B.
Box A contains balls numbered 1 through 9.
Box B contains balls numbered 1 through 5.
A box is chosen at random,and a ball is picked up from the box.
If the ball has odd number,then the next ball is picked up from the same box.
Else
If the ball has even number,then the next ball is picked up from the other box.
Thus two balls are selected.
What is the probablility that both balls have even numbers.?.
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! There are two boxes A and B.
Box A contains balls numbered 1 through 9.
Box B contains balls numbered 1 through 5.
A box is chosen at random,and a ball is picked up from the box.
If the ball has odd number,then the next ball is picked up from the same box.
Else
If the ball has even number,then the next ball is picked up from the other box.
Thus two balls are selected.
What is the pr
probablility that both balls have even numbers.?.
CASE 1....BOX A IS CHOSEN FIRST.
PROBABILITY OF CHOOSING BOX A =1/2...A CONTAINS 5 ODD & 4 EVEN NUMBERS
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PROBABILITY OF CHOOSING EVEN NUMBER = 4/9
BOX B HAS 3 ODD & 2 EVEN NUMBERS.
PROBABILITY OF GETTING EVEN NUMBER IS 2/5
HENCE PROBABILTY OF GETTING 2 EVEN NUMBERS IN THIS CASE =(4/9)*(2/5)=8/45
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CASE 2...BOX B IS CHOSEN FIRST
PROBABILITY OF CHOOSING BOX B =1/2...B CONTAINS 3 ODD & 2 EVEN NUMBERS
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PROBABILITY OF CHOOSING EVEN NUMBER = 2/5
BOX A HAS 5 ODD & 4 EVEN NUMBERS.
PROBABILITY OF GETTING EVEN NUMBER IS 4/9
HENCE PROBABILTY OF GETTING 2 EVEN NUMBERS IN THIS CASE =(2/5)*(4/9)=8/45
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HENCE OVER ALL PROBBILITY OF GETTING 2 EVEN NUMBERED BALLS IS
(1/2)*(8/45)+(1/2)*(8/45)=8/45
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