Question

Suppose that you and your friend alternately play a game. Both of your and your friend’s chance of winning in each game is 0.5. All the outcomes are independent. Each of you will play 100 games. Estimate the probability that you will win at least 5 more games than your friend. Both Y and Z follows Bin(100, 0.5). Y = number of games you win Z = number of games your friend wins.

Answer #1

So, conditions of normal approximation are satisfied.

So, conditions of normal approximation are satisfied.

We define new random variable X as number of games won by me more than that of my friend.

i.e. _{
}

i.e. _{
}

So, our required probability is given by

Suppose that you and your friend alternately play a game. Both
of your and your friend’s chance of winning in each game is 0.5.
All the outcomes are independent. Each of you will play 100
games.
Estimate the probability that you will win at least 5 more games
than your friend.
Both Y and Z follows Bin(100, 0.5).
Y = number of games you win
Z = number of games your friend wins.

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