Question

It was discovered that only 20% of students attended all Zoom sessions this past semester. What is the probability that out of 8 randomly selected students, exactly 2 of them attended all Zoom sessions? State your answer as a rate with four decimal places. Answer: As the owner of a new tokeout (take-dway) restaurant, you discover 26% of your customers are strictly vegan (do not eat any animal products)

Answer 1

Answer: To find the probability of exactly 2 out of 8 randomly selected students attending all Zoom sessions, we can use the binomial probability formula:

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

Where:

P(X = k) is the probability of getting exactly k successes (students attending all Zoom sessions),

n is the total number of trials (number of students selected),

k is the number of successes (students attending all Zoom sessions) we want,

p is the probability of success in a single trial (probability that a student attended all Zoom sessions).

In this case, n = 8 (total number of students selected), k = 2 (number of students attending all Zoom sessions), and p = 0.20 (probability that a student attended all Zoom sessions).

Now, plug in the values and calculate:

P(X = 2) = (8 choose 2) * 0.20^2 * (1 - 0.20)^(8 - 2)

Using a calculator:

P(X = 2) = 28 * 0.04 * 0.262144 ≈ 0.0298

So, the probability of exactly 2 out of 8 randomly selected students attending all Zoom sessions is approximately 0.0298.

For the second question about the probability of a customer being strictly vegan:

The probability of a customer being strictly vegan is given as 26%. We can represent this as:

P(vegan) = 0.26

Note: There is no need to convert this to a rate with four decimal places, as the probability is already given as a percentage (26%).