Question

A coin is tossed 100 times, each resulting in a tail (T) or a head (H). If a coin results in a head, Roy have to pay Slim 500$. If the coin results in a tail, Slim have to pay Roy 500$. What is the probability that Slim comes out ahead more than $20,000?

Answer 1

A coin is tossed 100 times, each resulting in a tail or a head.

If a coin results in a head, roy has to pay $ 500, or viceversa.

so for slim to win for more than $ 20,000, he should win at least 70 games.

as (70 - 30) * 40 = 20000

Now expected number of wins for slim = 100 * 0.5 = 50

standard deviation of number of wins = sqrt(100 * 0.5 * 0.5) = 5

so here we have to find

P(x >= 70) = 1 - P(x < 70)

z = (70 - 50)/5 = 4

P(x > 70) =1 - P(z < 4)

P(z < 4) = 0.99997

P(x > 70) =1 - P(z < 4) = 1- 0.99997 = 0.00003