A very good poker player is expected to earn $1 per hand in $100/$200 Texas Hold'em. The standard deviation is approximately $32.

(a) What is the probability a very good poker player earns a profit (more than $0) after playing 50 hands in $100/$200 Texas Hold'em?

(b) What is the probability a very good poker player loses (earns less than $0) after playing 100 hands in $100/$200 Texas Hold'em?

(c) What proportion of the time can a very good poker player expect to earn at least $500 after playing 100 hands in $100/$200 Texas Hold'em? Hint: $500 after 100 hands is a mean of $5 per hand.

(d) Would it be unusual for a very good poker player to lose at least $1000 after playing 100 hands in $100/$200 Texas Hold'em?

(e) Suppose twenty hands are played per hour. What is the probability that a very good poker player earns a profit during a twenty-four hour marathon session?