Question

1. q and r are independent events. if $p(q)=\frac{1}{8}$ and $p(r)=\frac{2}{5}$ find $p(q \text{ and } r)$

\bigcirc \frac{21}{40}
\bigcirc \frac{1}{20}
\bigcirc \frac{19}{40}

Explanation:

Step1: Recall independent events formula

For independent events $Q$ and $R$, $P(Q \text{ and } R) = P(Q) \times P(R)$

Step2: Substitute given probabilities

$P(Q \text{ and } R) = \frac{1}{8} \times \frac{2}{5}$

Step3: Calculate the product

$P(Q \text{ and } R) = \frac{1 \times 2}{8 \times 5} = \frac{2}{40} = \frac{1}{20}$

Answer:

$\boldsymbol{\frac{1}{20}}$