Matt has a special coin where, when tossed, heads comes up 62% of the time.
He plays a gambling game with Roy.
Each time the coin is tossed, if it comes up heads, Roy pays Matt $500.
. . If it comes up tails, Matt pays Roy $500.
The coin is tossed 100 times.
What is the probability that Matt comes out ahead more than $9,000?
If Matt wins 59 games (and loses 41), he will win exactly $9,000.
To win more than $9,000, Matt must win at least 60 games.
So we have: .
The answer is the sum of these probabilities: .