C.15 Number of successive victories

Taro and Jiro played game that the victory or defeat was decided on every once by all means.

Taro started winning successive victories in Jiro, but he lost five consecutive games afterwards and thereafter finished a game by five successive victories.

Winning rate (ratio of the number of the victories for the number of games) of Taro was 0.8.

Find the number of times that Taro won successive victories first.



Answer
15 times

Solution
As it is stated in a problem sentence that Taro started winning successive victories in Jiro, but he lost five consecutive games afterwards and thereafter finished a game by five successive victories, it is found that the number of times Taro lost is five times.

In addition, as for the rate of lost (ratio of number of lost for the number of total games) is 1 - 0.8 = 0.2. 

The number of total games can be calculated by 5 times / 0.2 = 25.

Therefore, the number of times that Taro won successive victories first is 25 - 5(five straight defeats) - 5(five successive victories) = 15.