Question

The 1899 Cleveland Spiders were a historically awful baseball team, finishing with a win-loss record of 20-134. So, assume that team would win any given game with probability 13%. Find the probability that the Spiders would have won their first three games played that season.

Answer 1

18% because 20+3=23 and 134-3=131 and so you divide 23/131 and you get 17.55 which rounds up to 18%

Answer 2

The probability that the Cleveland Spiders would have won their first three games is 0.00219.

Explanation:

Let's define a random variable X as follows:

`X_i =` "The Cleveland Spiders won the ith game"

`X_i =` can be either 1 or 0, 1 meaning that they won and 0 that they lost the game. We want the to compute the probability that they've won on the first, second and third game. In other words:

`P(X_1 \cap X_2 \cap X_3)`

Let's assume the events are independent, then:

`P(X_1 = 1 \cap X_2 = 1 \cap X_3 = 1) = P(X_1 = 1) * P(X_2 = 1) * P(X_3 = 1) = 0.13 * 0.13 * 0.13 = (0.13)^3 \approx 0.00219`