Question

Probability theory predicts that there is a 44% chance of a water polo team winning any particular match. If the water polo team playing 2 matches is simulated 10,000 times, in about how many of the simulations would you expect them to win exactly one match?

A. 2464
B. 1936
C. 3136
D. 4928

Answer 1

In simple terms, it’s 4928

Answer 2

After playing 2 matches possible outcomes are:
water polo team wins none, wins 1 or wins both games.

chance that they win both matches are:
0.44*0.44 = 0.1936 in relative value

Chance that they lose both matches are:
(1-0.44)*(1-0.44) = 0.3136 in relative value

If we multiply these relative values by number of matches and subtract that from number played double games (10000) we will get number of times they won only once.

10000 - 10000* (0.3136+ 0.1936) = 4928

Answer is D.