Question

cording to a recent survey, 80% of students are planning to attend at least one football game at their university. If a random sample of 10 students is selected, what is the probability that at least 9 of those students are planning to attend at least one game? (a) 0.1074 (b) 0.1342 (c) 0.3490 (d) 0.3758 (e) 0.5000

Answer 1

The probability that at least 9 out of 10 students are planning to attend at least one football game is approximately 0.1074.

Step-by-step explanation:

To find the probability that at least 9 out of 10 students are planning to attend at least one football game, we can use the binomial probability formula.

Let's define a success as a student planning to attend a game, and the probability of success is 0.8. The probability of failure, or a student not planning to attend, is 0.2.

Now, we can calculate the probability using the formula:

P(X ≥ k) = P(X = k) + P(X = k+1) + ... + P(X = n)

where X is the number of students planning to attend.

In this case, k = 9, n = 10, and P(X = k) = (10C9)*
`(0.8)^9*(0.2)^{(10-9)`.

Calculating all the probabilities and summing them up, we get the answer as approximately 0.1074. So, the correct option is (a) 0.1074.