Video: Using a Two-Way Frequency Table to Determine the Probability of Complement of Event

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.

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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.

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