Question

8 q and r are independent events if $p(q) = \frac{1}{4}$ and $p(r) = \frac{1}{5}$, find $p(q \text{ and } r)$.\
\bigcirc \quad $\frac{1}{20}$\
\bigcirc \quad $\frac{2}{5}$\
\bigcirc \quad $\frac{9}{20}$

Explanation:

Step1: Usar fórmula de eventos independientes

Para eventos independientes $Q$ y $R$, $P(Q \text{ and } R) = P(Q) \times P(R)$

Step2: Sustituir los valores dados

$P(Q \text{ and } R) = \frac{1}{4} \times \frac{1}{5}$

Step3: Calcular el producto

$P(Q \text{ and } R) = \frac{1 \times 1}{4 \times 5} = \frac{1}{20}$

Answer:

$\frac{1}{20}$