Question

A marine scientist has six ocean water samples that are evenly split between the Pacific and Atlantic oceans. Four of the ocean water samples are chosen using simple random sampling. Find the probability that all the Pacific ocean samples are chosen. 1/20

1/10
1/5
1/4

Answer 1

The probability of choosing all the Pacific ocean samples when four out of six samples are chosen at random is 1/5.

Step-by-step explanation:

To find the probability that all Pacific ocean samples are chosen from the six samples (three from the Pacific and three from the Atlantic) when four samples are chosen at random, we can use combinatorial methods.

There is a total of one way to choose all three Pacific samples, and we also need to choose one Atlantic sample from the remaining three. The number of ways to choose one Atlantic sample is 3.

The total number of ways to choose four samples from six is the combination of 6 taken 4 at a time, which is calculated as:

C(6, 4) = 6! / (4!*(6-4)!) = (6*5) / (2*1) = 15

So the probability of choosing all Pacific samples is:

P(all Pacific) = (Number of ways to choose all Pacific samples and one Atlantic sample) / (Total number of ways to choose any four samples) = (1*3) / 15 = 3 / 15 = 1/5