Question

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
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

Answer 1

Of the 870 boys, (2/3)(870) = 580 study Spanish.

Of the 800 girls, (3/5)(800) = 480 study Spanish.

So 1,060 of the 1,670 students study Spanish, meaning 1,670 - 1,060 = 610 of the 1,670 students do not study Spanish.

The probability that a student chosen at random from the whole school does not study Spanish is 610/1,670 = 61/167.