# 11.4.1. Calculating Probability

Given that 200 people of different nationalities participated in a conference, and their data is as shown in the table below, determine the probability that the chosen person is an English or Arabic speaker.

ParticipantArabic SpeakerEnglish SpeakerFrench SpeakerTotal Sum
Man40302595
Woman303540105
Sum706565200

• A
0.675
• B0.65
• C0.35
• D
0.325

### Example

Given that 200 people of different nationalities participated in a conference, and their data is as shown in the table below, determine the probability that the chosen person is an English or Arabic speaker.

ParticipantArabic SpeakerEnglish SpeakerFrench SpeakerTotal Sum
Man40302595
Woman303540105
Sum706565200

### Solution

The probability of event occurring is equal to the number of favorable outcomes divided by the total number of possible outcomes in the sample space, . In this case, event is selecting an English speaker. Find the probability of event as follows:

The probability of event occurring is equal to the number of favorable outcomes divided by the total number of possible outcomes in the sample space, . In this case, event is selecting an Arabic speaker. Now find the probability of event .

The notation refers to the probability of either event or event occurring. Also, the events and must be mutually exclusive, because the sum of the numbers of English speakers, Arabic speakers, and French speakers equals the total number of participants in the conference. If and are two mutually exclusive events, then . Next, use this fact to determine the probability of .

Thus, the probability of selecting an English speaker or an Arabic speaker is 0.675.

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