Question

Assume you bet $1 100 times on red (there are 38 equally likely slots and 18 are red). If red comes up you win $1, otherwise you lose your $1. (a) What are your expected winnings? (b) What is the probability that you are ahead after 100 bets? (c) What is the probability that you have lost $100

Answer 1

Given that

No. of Red slots = 18

No. of other slots = 20

so, the probability of Red P(R) = 18/38

the probability of other P(X) = 20/38

(A)

The expected winnings E(W) = [+ $1 *P(R) ] + [ - $1 *P(X)]

= 1*(18/38) - 1*(20/38)

= - $2/38

= - $0.0526

Hence, The expected winnings are loss $0.0526.

(B)

The only way a player will be ahead after 100 bets if he has won at least 51 of the 100 bets.

Thus, the probability that you are ahead after 100 bets

= 0.265

Hence, the probability that you are ahead after 100 bets is 0.265.

(C)

The probability that you have lost $100

= 1.332* e^-28