Question

Use the scenario below to determine the correct values of n, p, q and x of the binomial distribution.

Suppose that in a certain video game there is a 1.9% item drop rate of frozen rain after defeating a Frigid Element.
What is the probability that 2 frozen rains will drop if 20 Frigid Elements are defeated?
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Answer 1

In this scenario, we can use the binomial distribution to calculate the probability of getting 2 frozen rain drops after defeating 20 Frigid Elements. The binomial distribution has four parameters: n, p, q, and x.

- n is the number of trials or attempts, which is 20 in this case.

- p is the probability of success on each trial, which is 0.019 (1.9%) in this case.

- q is the probability of failure on each trial, which is 1 - p = 0.981.

- x is the number of successes we are interested in, which is 2 in this case.

Using the formula for the binomial distribution, we can calculate the probability of getting exactly 2 frozen rain drops:

P(X = 2) = (20 choose 2) * (0.019)^2 * (0.981)^(20-2)

where (20 choose 2) = 20! / (2! * (20-2)!) = 190 is the number of ways to choose 2 Frigid Elements out of 20.

Simplifying the formula, we get:

P(X = 2) = 190 * 0.019^2 * 0.981^18 = 0.261

Therefore, the probability that 2 frozen rains will drop if 20 Frigid Elements are defeated is approximately 0.261.