A and B toss a coon alternatively till one pf them tosses a head and eins the game. If A starts the game, find their respective probabilities of winning.
Answers
The probability of a winning = 2/3 & b winning = 1/3
Step-by-step explanation:
Case 1 : a gets Head - Then a wins 1/2
Case 2 : a gets tail - (1/2) then b get a chance to toss
then b can get Head or Tail
if b get Head - (1/2)(1/2) = 1/4 Chances to win
(1/4) chances to get tail Then games continues
a Has chance of winning 1/8
b has chance of winning = 1/16
and so on games continues until some one wins
a winning chances = 1/2 + 1/8 + ..............
= (1/2)/(1 - 1/4)
= (1/2)/(3/4)
= 2/3
b winning chance = 1/4 + 1/16 +........................
(1/4)/(1 - 1/4)
= (1/4)/(3/4)
= 1/3
Chances of winning a = 2/3 & b = 1/3
the probability of a winning a = 2/3 & b = 1/3
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