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PGEE 2018

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Three person plays a game by tossing a coin, if atleast one of the outcome is different from another end is declared, coins are biased with probability of head is 1/4 what is probability that game ends in first round
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9 votes
9 votes
P(H)=$1/4$

P(T)=$3/4$

Game ends after first round =1-Game does not end in first round

Game does not end in first round = All 3 gets same head/tail

=All gets head+ All gets tail

=$1/4*1/4*1/4 +3/4+3/4+3/4$

=$1/64 +27/4$

=$28/64$

Game ends after first round = $1-28/64$

=$36/64$

=$.5625$
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Game can end in the following four cases:

HHT: 3/64

HTH: 3/64

THH: 3/64

TTH: 9/64

THT:9/64

HTT:9/64

Add them all up: 36/64 = 9/16
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