# A red container contains 7 items of which 2 are new and 5 are old items. A purple container contains 4 items of which 1 is new and 3 are old items. An item is drawn at random from each box. 1. What is the probability that both items are old items?

## What is the probability that one item is new and one item old?

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Mar 13, 2018

Two old items: $\frac{15}{28} \approx 0.5357$
One old item: $\frac{11}{28} \approx 0.3929$

#### Explanation:

The draw from the red container for an old item has a probability of $\frac{5}{7}$ of being successful.

The draw from the purple container for an old item has a probability of $\frac{3}{4}$ of being successful.

This means that there is a $\frac{5}{7} \times \frac{3}{4} = \frac{15}{28} \approx 0.5357$ probability that both items will be old.

For finding where one item is old, we can look at the probability of the old item being drawn from the red container and a new item from the purple container $\left(\frac{5}{7} \times \frac{1}{4} = \frac{5}{28}\right)$ and adding that to the probability of the old item being drawn from the purple container and a new item from the red container $\left(\frac{2}{7} \times \frac{3}{4} = \frac{6}{28}\right)$, giving:

$\frac{5}{28} + \frac{6}{28} = \frac{11}{28} \approx 0.3929$

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