# 11.4.1. Calculating Probability

200 people of different nationalities participated in a conference, and their data is as shown in the table. Determine the probability that the chosen person is an Arabic-speaking man or an English-speaking woman.

ParticipantArabic SpeakerEnglish SpeakerFrench SpeakerTotal Sum
Man25401580
Woman404040120
Sum658055200

• A
0.325
• B0.4
• C
0.725
• D
0.275

### Example

200 people of different nationalities participated in a conference, and their data is as shown in the table. Determine the probability that the chosen person is an Arabic-speaking man or an English-speaking woman.

ParticipantArabic SpeakerEnglish SpeakerFrench SpeakerTotal Sum
Man25401580
Woman404040120
Sum658055200

### 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 Arabic-speaking man. 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 English-speaking woman. Now find the probability of event .

The notation refers to the probability of either event or event occurring. If and are two mutually exclusive events, then . Next, use this fact to determine the probability of .

Thus, the probability of selecting an Arabic-speaking man or an English-speaking woman is 0.325.

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