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Problem :
A coin is flipped 10 times consecutively. What is the probability that the sixth flip results in a head ?
What is the probability that the 10th flip is a tail ?
Solution :
When a coin is flipped, there is equal possibility for head and tail in each flip for a fair coin. Hence whichever flip it be the probability is 1/2 because each event is independent and mutually exclusive and exhaustive.

A basket has three red balls and three white balls. So how many minimum balls must you draw to make a pair of two balls with the same colour ?
Solution : Atleast three balls have to be drawn to ensure that the pair is obtained in any case. How & why not Two? If the first two drawn balls differ in colour, then the third ball is a tie breaking situation between the two coloured balls and whichever colour you get in the third draw, you atleast make a full pair then.
If 10 workers build a wall in 3 days. In how many days will 15 workers build the same wall. ?
Solution :
None. Well, the wall is already built. :) But mathematically working it will be 2 days.

A and B play a game and roll a dice. The one who gets a six will win the game. What is the probability of B's winning the game.
A can win the game in 1st or 3rd or 5th or 7th try.
P(A) = P(A) + P'(A) P'(B) P(A) + P'(A) P'(B) P'(A) P'(B) P(A) +  . . . . .
= 1/6 + 5/6*5/6*1/6 +5/6*5/6*5/6*5/6*1/6+ . . . .
= 1/6 (1+ 5/6*5/6 + 5/6*5/6*5/6*5/6+.......)          This forms an infinite GP series
=1/6 (   1/(1-(5/6*5/6))   )
= 1/6 (  36/36-25)   )
= 1/6 (36/11)

So P(B) = 1-(PA) = 1 - 6/11

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