Question

Binomial Distribution

Tom and Jerry play one game per day. It is known that Tom’s winning chance is P[W] = 0.6 and if he does not win, then he loses. Game results are assumed to be independent. After FOUR days, variable T indicates a total number of games won by Tom. So J = 4 − T is the number of games he lost (or Jerry won).

Use the formula for binomial probabilities and probability rules to answer questions below.

1. Find the chance that Tom loses exactly one game,

   P (J = 1)

2. Evaluate probability that Tom wins at least two games,

   P [T ≥ 2]

3. Determine the chance than Jerry wins two or more games,

   P [J ≥ 2]

4. Find expected number of games won by Tom,

   E[T]

5. Use the formula for variance to determine the variance of T, that is

   Var[T]

6. Assume that after a game is over, the winner gets $1 from his partner. Thus the variable of interest is the balance for Tom, which is B = T − J. Evaluate the expected balance,
   E[B]

7. Derive the variance of B, that is Var[B]

Answer 1