A,B,C,D,E play the following game.each person picks one card from card numbered 1 through 10.the person who picks the greatest numbered card loses and is out of the game.now the remaining four return their cards to the packk and draw again and again the person with the greatest numbered card loses.this process is repeated till only one person is left in the game who is declared as the winner.what is the probability that A is the winner?
a) 3/4 b)4/17 c)1/5 d)5/24
Answers
Given : A, B, C, D and E play the following game. Each person picks one card from cards numbered 1 through 10. The person who picks the greatest numbered card loses and is out of the game. Now the remaining four return their cards to the pack and draw again, and until one player left
To Find : Probability that A is winner
Solution:
Simple method : 5 players
Each have equal chance to win
hence 1/5
Probability that A is the winner = 1/5
Detailed method
A is the winner if he did not lose any game
in 1st game 5 players
Probability that A looses = 1/5
Probability that A does not loose = 1 - 1/5 = 4/5
in 2nd game 4 players are there
Probability that A looses = 1/4
Probability that A does not loose = 1 - 1/4 = 3/4
in 3rd game 3 players are there
Probability that A looses = 1/3
Probability that A does not loose = 1 - 1/3 = 2/3
in 4th game 2 players are there
Probability that A looses = 1/2
Probability that A does not loose = 1 - 1/2 = 1/2
Probability that A wins = (4/5) (3/4) (2/3) ( 1/2)
= 1/5
Probability that A wins = 1/5
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