Question

Please help! Correct answer only!

Juan and his stepmother wanted to start volunteering together. They found 8 opportunities online, 3 of which involved working in nature.
If they randomly applied to 4 of the opportunities in a specific order, what is the probability that just the first 2 of the chosen opportunities involve working in nature?

Write your answer as a decimal rounded to four decimal places.

Answer 1

0.0714

Explanation:

The probability that the first is "working in nature" is 3/8.

The probability that the 2nd is "working in nature" is 2/7.

The probability that the 3rd is "not working in nature" is 5/6.

The probability that the 4th is "not working in nature" is 4/5.

Thus the probability that the first two of 4 opportunities are "working in nature" is ...

(3·2·5·4)/(8·7·6·5) = 1/14 ≈ 0.0714