Question

A tin of nuts contains 23 cashews, 20 pecans, 13 peanuts, and 10 pistachios. Find the probability of reaching in and selecting a pecan and then a cashew. Assume the nuts are chosen without replacement. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

Answer 1

[AI-generated answer — Bot GPT 3.5]

First, determine the total number of nuts in the tin:

23 + 20 + 13 + 10 = 66 nuts

The probability of selecting a pecan on the first draw is:

20 pecans / 66 total nuts = 10 / 33

Since the nuts are chosen without replacement, there are now 65 nuts left in the tin. The probability of selecting a cashew on the second draw, given that a pecan was already selected, is:

23 cashews / 65 total nuts = 23 / 65

Therefore, the probability of selecting a pecan and then a cashew is:

(10 / 33) * (23 / 65) = 230 / 2145 ≈ 0.107 or 0.107 to the nearest millionth.