Question

A survey shows that about 60 s (L.e., 0.6) of all stiadents know the Help fourMath foufibe channel in a college Suppose that we randomly select 17 students from the college, please solve the follewing problems and round your answers to 4 decimal places.

Answer 1

It looks like you have a probability problem involving the knowledge of students about a particular channel. To solve this problem, 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 exactly k students knowing about the Help fourMath foufibe channel.

- n is the total number of students selected (17 in this case).

- k is the number of students who know about the channel.

- p is the probability that a single student knows about the channel (0.6 in this case).

- (n choose k) is the binomial coefficient, which can be calculated as C(n, k) = n! / (k! * (n - k)!).

Let's solve the following problems:

1. Probability that exactly 10 students know about the Help fourMath foufibe channel (k = 10):

P(X = 10) = (17 choose 10) * (0.6)^10 * (1 - 0.6)^(17 - 10)

First, calculate the binomial coefficient:

(17 choose 10) = 17! / (10! * (17 - 10)!) = 6188

Now, plug the values into the formula:

P(X = 10) = 6188 * (0.6)^10 * (0.4)^7

Calculate this to get the answer.

2. Probability that more than 12 students know about the Help fourMath foufibe channel (k > 12):

P(X > 12) = P(X = 13) + P(X = 14) + ... + P(X = 17)

You can calculate each of these individual probabilities using the formula and then sum them up.

Remember to round your answers to 4 decimal places as requested.

Explanation: