A person invested 2000 in two different accounts. One account earns 5% interest per year, and the other earns 7% interest per year. If the total interest earned in one year is 120, how much was invested in each account?

Step 1: Calculate the percentages for each category using the given information. Let F be Football, H be Hockey, and B be Basketball. Given: $P(F) = 0.60$ $P(H) = 0.45$ $P(B) = 0.40$ $P(F \cap H) = 0.30$ $P(F \cap B) = 0.20$ $P(H \cap B) = 0.15$ $P(F \cap H \cap B) = 0.10$

First, calculate the percentages of playing exactly two games: $P(F and H only) = P(F \cap H) - P(F \cap H \cap B) = 0.30 - 0.10 = 0.20$ $P(F and B only) = P(F \cap B) - P(F \cap H \cap B) = 0.20 - 0.10 = 0.10$ $P(H and B only) = P(H \cap B) - P(F \cap H \cap B) = 0.15 - 0.10 = 0.05$

Next, calculate the percentages of playing exactly one game: $P(F only) = P(F) - (P(F and H only) + P(F and B only) + P(F \cap H \cap B))$ $P(F only) = 0.60 - (0.20 + 0.10 + 0.10) = 0.60 - 0.40 = 0.20$ $P(H only) = P(H) - (P(F and H only) + P(\text{H and B only