Respuesta :
Answer:
63.64%
Step-by-step explanation:
Let P(M) be the percentage of students enrolled in a mathematics course
Let P(C) be the percentage of students enrolled in a Computer Science (CS) course.
We are told that One-fifth of those taking a mathematics course arealso taking a computer science course.
Thus, we can write that as:
P(M|C) = 1/5,
We are also told that one-seventh of those taking a computer science course are also taking a mathematics course.
Thus, we can write it as;
P(C|M) = 1/7
According to sets notations, P(M ∩ C) will be the probability that any student is enrolled in both Maths and Computer Science.
Thus;
P(M ∩ C) = P(M|C)P(C) = (1/5)P(C)
Also,
P(M ∩ C) = P(C|M)P(M) = (1/7)P(M)
Equating them, we have;
(1/5)P(C) = (1/7)P(M)
P(C) = (5/7)P(M)
Now; P(M U C) = 1
Let's express out P(M U C)
P(M U C) = P(M) + P(C) - P(M ∩ C) = P(M) + (5/7)P(M) - (1/7)P(M) = (11/7)P(M)
1 = (11/7)P(M)
P(M) = 7/11 = 0.6364 or 63.64%
