In a population of 328 snakes at a zoo, it is known that 162 are female. A scientist selected 50 snakes at random to run some tests. What is the probability that the scientist will select at least 30 female snakes?

To calculate the probability, we need to determine the total number of ways that the scientist can select at least 30 female snakes out of 50.

First, let's calculate the probability of selecting exactly 30, 31, 32, ... , 50 female snakes.

For each number of female snakes selected, we need to calculate the probability of selecting that number of females and then multiply it by the probability of selecting the remaining (50 - number of females) snakes as males.

The probability of selecting a female snake is given by the ratio of the number of female snakes to the total number of snakes: p(female) = 162/328.
Similarly, the probability of selecting a male snake is given by: p(male) = 1 - p(female).

Now, let's calculate the probabilities for each scenario and sum them up to find the probability of at least 30 female snakes.

P(at least 30 females) = P(30) + P(31) + P(32) + ... + P(50)

To calculate P(30), we multiply the probability of selecting 30 females by the probability of selecting (50 - 30) = 20 males:
P(30) = (162/328)^30 * (1 - 162/328)^20

We repeat this calculation for all numbers from 30 to 50, and add up the results to get the final probability.