The table shows the responses from 110 people when they were asked how many
additional languages they spoke on top of their mother tongue. Given that a person is chosen at random from the group, that speaks at least one
additional language, what is the probability that they will be male?
We know that the probability of an event is the number of ways that event can occur
over all possible outcomes. We want to know the probability that we would choose a male. But we have to be careful here and consider which group we’re selecting from. The person chosen at random is being selected from the people that speak at least one
additional language. On the table, that is the males and females that speak one, two, or three plus
languages. Our denominator should be the people that speak one, two, or three plus additional
We could add all six of the values in this rectangle. However, we already know the total from column one, two, and three plus. Instead, we can just add 30 plus 20 plus 20. We want to know the ways that we can choose a male out of this group. There are 12 plus nine plus 12 males in the group. We need to add up the number of males that speak one, two, or three plus additional
languages. When we do that, we get 33 over 70.
The probability that a person chosen at random from the group of people that speaks
at least one additional language is 33 out of 70.