An environmental scientist obtains a sample of water from an irrigation canal that contains a certain type of bacteria at a concentration of 4 per milliliter. What is the probability that there will be Exactly 8 bacteria in a 4-milliliter sample?
A) 0.0298
B) 0.0120
C) 0.0060
D) 0.9940

Question

Quizplus · Accepted Answer

This is a binomial distribution problem, where we have a fixed number of trials (4 milliliters) and each trial can result in success (presence of bacteria) or failure (absence of bacteria). The probability of success in each trial is given as 4 bacteria per milliliter, which means the probability of failure is 1 - (4/1000) = 0.996.

To find the probability of getting exactly 8 bacteria in a 4-milliliter sample, we can use the following formula:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where:
n = number of trials (4 milliliters)
p = probability of success in each trial (4/1000 = 0.004)
k = number of successes we want (8)

Using this formula, we get:

P(X = 8) = (4 choose 8) * 0.004^8 * 0.996^(4-8)
           = (4 choose 8) * 0.004^8 * 0.996^-4
           = (4! / (8! * (4-8)!)) * 0.004^8 * 0.996^-4
           = 0.0120

Therefore, the probability of obtaining exactly 8 bacteria in a 4-milliliter sample is 0.0120, which corresponds to choice B.

An Environmental Scientist Obtains a Sample of Water from an Irrigation