Question

If A and B are two events associated with a random experiment, then
$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$
If A, B, C are three events associated with a random experiment, then
$P(A\cup B\cup C)=P\left(A\right)+P\left(B\right)+P\left(C\right)-P(A\cap B)-P(B\cap C)-P(A\cap C)+P(A\cap B\cap C)$

Probability that Chakri passes in mathematics is $\frac{2}{3}$ and the probability that he passes in English is $\frac{4}{9}$. If the probability of passing both courses is $\frac{1}{4}$, what is the probability that Chakri will pass in atleast one of these subjects?

Answer 1

Probability of passing in Mathematics is $P\left(M\right)=\frac{2}{3}$.

Probability of passing in English is$P\left(E\right)=\frac{4}{9}$.

Probability of passing in both is$P(M\cap E)=\frac{1}{4}$.

$P(M\cup E)=P\left(M\right)+P\left(E\right)-P(M\cap E)=\frac{2}{3}+\frac{4}{9}-\frac{1}{4}=\frac{31}{36}$