At a technology conference, each of 420 attendees attended exactly one workshop. Each workshop was in either the design track or the data science track and was held either in the morning or in the afternoon. Of the attendees, 252 selected the design track.
Given that a randomly selected attendee was in the data science track, the probability that the attendee attended an afternoon workshop was . Given that a randomly selected attendee attended a morning workshop, the probability that the attendee selected the design track was .
What is the number of attendees who selected the design track and attended an afternoon workshop?
For a conditional-probability question involving two categories, organize the information as a two-way table, even if no table is provided. First use a condition based on a known track total to find one cell. Then reinterpret the other conditional probability as a fraction of its stated group. Once one part of that group is known, work backward to find the group total and the requested cell.
Hints
Find the other track total
Subtract the number of design attendees from 420 to find the number of data science attendees.
Split the data science attendees
Use to find how many data science attendees were in the afternoon. The rest attended in the morning.
Reverse the morning proportion
If of morning attendees selected design, then selected data science. Use the morning data science count to determine the total number of morning attendees.
Desmos Guide
Note the faster approach
A two-way table or the proportion calculations are faster by hand. Desmos can verify the total number of morning attendees.
Graph the two expressions
Enter and . The -coordinate of their intersection represents the number of morning attendees.
Calculate the remaining design attendees
Use the calculator to enter . This subtracts the design morning count from the total design count.
Step-by-step Explanation
Find the data science totals by time
The number of data science attendees was
Of these attendees, attended in the afternoon:
Therefore, the number of data science attendees in the morning was .
Use the morning conditional probability
Among morning attendees, selected design, so the remaining selected data science. Thus, 63 is of the morning total.
So the morning total was .
Find the design afternoon count
The number of design attendees in the morning was
Since there were 252 design attendees altogether, the number who attended in the afternoon was