Quick statistic question... I really don't understand. Thanks!!

Question

The opera house has 2000 seats. there are 1200 seats on the main floor and 800 in the balcony. 40% of those in the balcony buy a program while 50% of people on the main floor buy a program. on opening night of the lion king, every seat is taken. if an audience member is selected at random, what is the probability that he or she bought a program?

A. 22.5%
B. 42%
C. 46%
D. 90%
E. 92%

Answer 1

This statistics question tests whether you can do percents (math) and understand “selecting an audience member at random.”

Let’s consider the “full house” (every seat filled) on the opening night of The Lion King:

   The number of programs sold is:

                 0.40 * 800 = 320        (balcony)

                 0.50 * 1200 = 600       (main floor)

So, of the 2000 seats total, 920 bought programs.

If it is equally likely that we select any one of the 2000 patrons (could have a seat anywhere), then we have a 920 in 2000 chance of selecting a person who has bought a program.

    920 / 2000   =  0.46     or 46% probability that we select a person who bought a program