# You are playing a game with your friend. You win with 55% probability,

You are playing a game with your friend. You win with 55% probability, your friend 30%. There is no draw. You decide to play a series of games. What is your probability of winning the series if the player with
a) 5 wins?
b) 6 wins?
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Sarythe
Step 1
Here let the event of winning me is ${E}_{1}$
Let the event of winning my friend is ${E}_{2}$
The probability of winning mine $P\left({E}_{1}\right)=\frac{55}{100}=0.55$
The probability of winning of my friend $P\left({E}_{2}\right)=\frac{30}{100}=0.3$
Step 2
Now,
a) the probability of winning of mine if my friend win 5 times
$P\left({E}_{1}\right)-P\left({E}_{2}\right)×5=0.55-0.3×5=-0.95$
b) the probability of winning mine if my friends win 6 times
$P\left({E}_{1}\right)-P\left({E}_{2}\right)×6=0.55-0.3×6=-1.25$