# 11.4.1. Calculating Probability

The following table represents the data collected from 200 conference attendees of different nationalities:

ParticipantArabic SpeakerEnglish SpeakerFrench SpeakerTotal Sum
Man454025110
Woman20254590
Sum656570200

If a participant is selected, find his probability of speaking both Arabic and English.

• A0
• B0.2
• C0.1
• D
0.125

### Example

The following table represents the data collected from 200 conference attendees of different nationalities:

ParticipantArabic SpeakerEnglish SpeakerFrench SpeakerTotal Sum
Man454025110
Woman20254590
Sum656570200

If a participant is selected, find his probability of speaking both Arabic and English.

### Solution

In this case, event is selecting an Arabic speaker, and event is selecting an English speaker. Since the sum of the number of Arabic speakers, the number of English speakers, and the number of French speakers equals the total number of conference attendees, and must be mutually exclusive events. This means that they cannot occur together. The probability of both event and event occurring is equal to the number of outcomes favorable for both events divided by the total number of possible outcomes in the sample space, Find the probability of both event and event occurring as follows:

Thus, the probability of selecting a participant who speaks both Arabic and English is 0.

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