What is the probability, as a fraction in its simplest form, that a student chosen at random from the whole school does not study Spanish

Question

The part one of the question was:

There are 870 boys and 800 girls in a school. 

The probability that a boy chosen at random studies Spanish is 2/3

The probability that a girl chosen at random studies Spanish is 3/5

 

The answer to part A was 1060

Answer 1

The definition of probability is:  (number of successful outcomes) / (total number of outcomes)

     Note that this assumes that there is a uniform frequency distribution of outcomes and that the random selection is "fair."

 

870 boys:     P(boy studies Spanish) = 2/3 = 580/870

                   P(boy does NOT study Spanish) = 290/870     [note: don't reduce, for now]

 

800 girls:     P(girl studies Spanish) = 3/5 = 480/800

                   P(girl does NOT study Spanish) = 320/800

 

"What is the probability, as a fraction in its simplest form, that a student chosen at random from the whole school does not study Spanish?"

                   P(student does NOT study Spanish) = (290 + 320) / (870 + 800)

                   P(student does NOT study Spanish) = 610 / 1670

                   P(student does NOT study Spanish) = 61 / 167

Answer 2

There are 870 boys and 2/3 speak Spanish. So 580 (2/3 of 870) speak Spanish and 290 (870-580) do not.

 

Similarly, there are 800 girls and 3/5 speak Spanish. 480 speak Spanish and 320 don't.

 

There are 1670 student total and 610 don't speak Spanish