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Probability and conditional probability SAT question
Math · Problem-Solving and Data Analysis · Medium · Answer it here, explanation included.
At a conference, there are a total of attendees. Each attendee is assigned to either group A, group B, or group C. If one of these attendees is selected at random, the probability of selecting an attendee who is assigned to group A is and the probability of selecting an attendee who is assigned to group B is . How many attendees are assigned to group C?
Enter a number or fraction (like 3/17 or 0.176). Press Enter to check.
ExplanationShow
The correct answer is . It's given that there are a total of attendees and each attendee is assigned to either group A, group B, or group C. It's also given that if one of these attendees is selected at random, the probability of selecting an attendee who is assigned to group A is and the probability of selecting an attendee who is assigned to group B is . It follows that there are , or , attendees who are assigned to group A and , or , attendees who are assigned to group B. The number of attendees who are assigned to group C is the number of attendees who are not assigned to group A or group B. In other words, the number of attendees who are assigned to group C is the total number of attendees minus the number of attendees who are assigned to group A and group B. Therefore, the number of attendees who are assigned to group C is , or .
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