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)](https://tex.z-dn.net/?f=P%28X%20%5Ccap%20Y%29%20%20%3D%20%20P%28X%29%20%5Ccdot%20P%28Y%7CX%29)
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](https://tex.z-dn.net/?f=P%28X%27%5Ccap%20Y%29%20%3D%20P%28X%27%29P%28Y%7CX%27%29%20%5C%5CP%28X%27%5Ccap%20Y%29%3D%200.11%5Ctimes%200.23%20%3D%200.0253)
Hence, the correct option is d) 0.0253