# Suppose Q and R are independent events. What is P(Q and R) if P(Q) = 7/15 and P(R)=4/7?

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2
Jun 25, 2016

If $Q$ and $R$ are two independent events,
then $P \left(Q \mathmr{and} R\right) = P \left(Q\right) \times P \left(R\right) = \frac{4}{15}$ - however there is an issue.

#### Explanation:

If $Q$ and $R$ are two independent events, then

$P \left(Q \mathmr{and} R\right) = P \left(Q\right) \times P \left(R\right)$

and hence in the given instant

$P \left(Q \mathmr{and} R\right) = \frac{7}{15} \times \frac{4}{7} = \frac{4}{15}$

However, in the given case it is observed that

$P \left(Q\right) + P \left(R\right) = \frac{7}{15} + \frac{4}{7} = \frac{7 \times 7 + 15 \times 4}{15 \times 7} = \frac{109}{105}$

this is greater than one, meaning thereby that $Q$ and $R$ are not independent event.

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