# The box contains 80 parts, 70 of which are standard. At random, two parts are extracted in turn. Find the probability

August 3, 2020 | Education

| **The box contains 80 parts, 70 of which are standard. At random, two parts are extracted in turn. Find the probability that both extracted parts are standard if:**

**1) the first part is returned back to the box before removing the second;**

**2) the first part is not returned to the box.**

Consider the events:

A – the appearance of a standard part in the first test;

B – appearance of a standard part in the second test.

Then AB – both parts are standard.

1) In the first case, events A and B are independent and P = 70/80 * 70/80 = 0.77

2) In the second case, events A and B are dependent. If A happened, then 79 parts will remain in the box, and there will be 69 standard parts and then P = 69/79 = 0.87

Then 70/80 * 69/79 = 0.76

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