Find the probability that Mensah passes both Mathematics and Economics, given the individual probabilities and the probability of passing at least one.

Let $P(M)$ be the probability that Mensah passes Mathematics.
Let $P(E)$ be the probability that Mensah passes Economics.
Let $P(M \cup E)$ be the probability that Mensah passes at least one subject.
We are given:
$P(M) = \frac{3}{4}$
$P(E) = \frac{5}{8}$
$P(M \cup E) = \frac{7}{12}$

The formula for the probability of the union of two events is:

where $P(M \cap E)$ is the probability that Mensah passes both subjects.

The least common multiple (LCM) of 4, 8, and 12 is 24.
Convert each fraction to have a denominator of 24:
$\frac{3}{4} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24}$
$\frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24}$
$\frac{7}{12} = \frac{7 \times 2}{12 \times 2} = \frac{14}{24}$

Now substitute these equivalent fractions back into the equation:

The probability that Mensah passes both subjects is $\frac{19}{24}$.