Question

Seniors at a certain high school took a survey regarding future plans. All plan to attend college some time; however, 77% plan to go to college immediately following high school. Of those who plan to attend college immediately following high school, 18% plan to major in Math. Of those who do not plan to attend college immediately following high school, 11% plan to major in Math. What is the probability that a randomly chosen senior does not plan to attend college immediately following high school and plans to major in Math.
a) 0.1386
b) 0.1800
c) 0.8900
d) 0.0253
e) 0.1100
f) None of the above.

Answer 1

Answer:

The correct option is d) 0.0253

Step-by-step explanation:

Consider the provided information.

When two events, X and Y, are dependent, then the probability of both occurring is: $P(X \cap Y)  =  P(X) \cdot P(Y|X)$

All plan to attend college some time; however, 77% plan to go to college immediately following high school.

Let X represents the Plan to go to college.

P(X) = 0.77

P(X') = 1 - 0.77 = 0.23

Of those who plan to attend college immediately following high school, 18% plan to major in Math. Of those who do not plan to attend college immediately following high school, 11% plan to major in Math.

Let Y represents Major in Math.

P(Y|X) = 0.18 and P(Y|X') = 0.11

Therefore the required probability is:

$P(X'\cap Y) = P(X')P(Y|X') \\P(X'\cap Y)= 0.11\times 0.23 = 0.0253$

Hence, the correct option is d) 0.0253