Answer:
0.046145 = 4.6145%
Step-by-step explanation:
We need to find the probability of 19 or 20 (all) students considering calculus to be an exciting subject, so first we find the probability for 19 students, then for 20 students, and we sum these probabilities.
The probability of the student NOT considering calculus to be an exciting subject is 1 - 0.78 = 0.22
For 19 students, we also have to calculate a combination of 20 choose 19, as these 19 students can be in different "position" among the 20 students, so:
C(20,19) = 20!/19! = 20
Probability of 19 students considering calculus to be an exciting subject:
C(20,19) * 0.78^19 * 0.22^1 = 0.039196756
Probability of 20 students considering calculus to be an exciting subject:
C(20,20) * 0.78^20 = 1 * 0.78^20 = 0.006948516
The final probability is:
0.039196756 + 0.006948516 = 0.046145272 = 4.6145272%
Rounding to six decimal places: 0.046145 = 4.6145%
The probability that 19 or more students find calculus exciting is P = 0.046146
We can think this as:
P = Probability that 1 student does not find calculus exciting + Probability that no student does not find calculus exciting
If 78% of the students like calculus, then 22% do not.
The first one will be given by:
P = 20*(0.78)^19*(0.22)^1 = 0.039197
Where the factor of 20 comes by the permutations, as any of the 20 students can be the one that does not like calculus.
The probability that no student does not like calculus is:
P' = (0.78)^20 = 0.006949
Adding these two we get:
p = P + P' = 0.039197 + 0.006949 = 0.046146
If you want to learn more about probability, you can read:
https://brainly.com/question/251701
