The parents of 7 out of every 10 students in a class are farmers. If 12 students were selected at random, find the probability that the parents of 8 of them will be farmers.
- 0.0078
- 0.0231
- 0.0780
-
0.2311
The correct answer is: D
Explanation
P(farmer parent) = \(\frac{7}{10}\) = 0.7
P(non- framer parent) = 1 - 0.7 = 0.3
Using, \(_x^nC p^x q^{n - r}\)
for 12 students, the probability that 8 of their parents will be farmers is:
P\(_8\) = \(_x^nC p^x q^{n - r}\) = \(_8^{12}C (0.7^8 (0.3)^{12 - 8}\)
P\(_8\) = \(\frac{12!}{8!4!}\)(0.7)\(^8\)(0.3)\(^4\) = 0.2311