# Urn 1 contains 7 red balls and 1 black ball. Urn 2 contains 5 red balls and 3 black balls. Urn 3...

## Question:

Urn 1 contains 7 red balls and 1 black ball. Urn 2 contains 5 red balls and 3 black balls. Urn 3 contains 2 red balls and 4 black balls.

If an urn is selected at random and a ball is drawn, find the probability that it will be red. (Enter your answer as a fraction or a decimal rounded to 3 decimal places).

## Total Probability:

The law of total probability basically breaks up calculations of probabilities into several distinct parts. Suppose we want to calculate the probability of an event A but don't have enough information to do so. The law of total probability requires that we have a set of disjoint events whose union is A. The probability of A is then equal to the sum of the probabilities of these disjoint events.

The probability of selecting an randomly is {eq}\frac{1}{3}. {/eq} By the law of total probability,

{eq}\begin{align*} P(\text{red}) &=...

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