Question

You do not replace the t-shirt; you choose and choose another (also without looking). What is the probability that you choose brown both times? Provide the formula or reasoning for calculating this probability and explain the concept of sampling without replacement in probability scenarios.

Answer 1

The probability of choosing brown t-shirts without replacement both times can be calculated using the concept of sampling without replacement.

The probability of choosing brown t-shirts without replacement both times can be calculated using the concept of sampling without replacement.

When sampling without replacement, each member of a population can be chosen only once, and the events are considered to be dependent.

The probabilities for the second pick are affected by the result of the first pick.

To calculate the probability, let's assume there are 5 brown t-shirts and a total of 20 t-shirts.

For the first pick, the probability of choosing a brown t-shirt is 5/20.

Then, since we did not replace the t-shirt, for the second pick, the probability of choosing another brown t-shirt is 4/19.

Therefore, the probability of choosing brown t-shirts without replacement both times is (5/20) * (4/19) = 1/19 = 0.0526 (rounded to four decimal places).