Video Transcript
The table represents the data
collected from 200 conference attendees of different nationalities. Find the probability that a
randomly selected participant does not speak English.
The rows in our table tell us
whether the participant was male or female. The columns tell us which language
they speak, whether they speak Arabic, English, or French. We are told in the question that
there are a total of 200 attendees. If we let 𝐸 be the event that the
conference attendee speaks English, we can calculate the probability of event
𝐸. This will be the number of
attendees that speak English out of the total number of attendees.
There are 35 men who speak English
and 30 women, giving us a total of 65 people. The probability that a randomly
selected participant speaks English is 65 out of 200 or sixty-five two
hundredths. We are interested in the
probability that the participant does not speak English. This is known as the
complement. We know that the probability of any
complementary event, 𝐴 bar, occurring is equal to one minus the probability of
𝐴. In this question, the probability
of 𝐸 bar, the participant not speaking English, is equal to one minus 65 out of
200. This is equal to 135 out of
200.
We can simplify this fraction by
dividing the numerator and denominator by five. 135 divided by five is 27 and 200
divided by five is equal to 40. The probability that a randomly
selected participant does not speak English is 27 out of 40 or twenty-seven
fortieths. We could also write this answer as
a decimal by firstly considering the fraction 135 out of 200. Dividing the denominator by two
gives us 100. If we divide the numerator by two,
we get 67.5 as a half of 100 is 50 and a half of 35 is 17.5. Dividing 67.5 by 100 gives us
0.675. The probability that the randomly
selected participant does not speak English, written as a decimal, is 0.675. We could also write this as a
percentage by multiplying 100, giving us 67.5 percent.
