You are given a math word problem and you are supposed to make use of mathematical concepts like probability, combinatorics, linear equations, sequences/series, or simple operators like addition, subtraction, division, or multiplication to answer the given question. Choose the best option from the 5 given options and report that option.

[Q]: Question: The average age of students in section A of 100 students is 20 years and the average age of students in section B of 150 students is 30 years. Find the average age of students in both sections taken together?

 Option A: 26 years

 Option B: 30years

 Option C: 15years

 Option D: 25years

 Option E: 20years
[A]: Option A


[Q]: Question: Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 9?

 Option A: 2

 Option B: 3

 Option C: 1

 Option D: 6

 Option E: 4
[A]: Option D


[Q]: Question: Given that E and F are events such that P(E) = 10 P(F) = 2 and P(E n F) = 10,
find P (E|F) and P(F|E)

 Option A: 1

 Option B: 69

 Option C: 24

 Option D: 5

 Option E: 12
[A]:
Option D