A conditional probability is a chance calculated after a condition limits who can be selected. The cue is “selected from” a particular group. Find how many people in each original group meet that condition, then use their combined count as the denominator. Dividing by everyone surveyed instead answers a different question.
Hints
- Hint 1
A percent describes a part of a particular group. The is taken only from the members who attended training. How many of the attenders signed up to mentor?
- Hint 2
Before finding the other mentor count, find how many members did not attend by subtracting the attenders from all surveyed members. Take of that remaining group, not of all members.
- Hint 3
The words “selected at random from the members who signed up” limit who can be picked. Add the mentor counts from both training groups to find the denominator; the numerator is the mentors who attended.
Step-by-step
Count the mentors, then restrict the selection
Step 1Find the mentors who attended training
The attenders are the base, the group this percent is taken of. Type in Desmos. It shows , so members who attended training signed up to mentor.
- Step 2
Find the mentors who did not attend
There were members who didn't attend. The applies only to those . Type in Desmos; it shows members who didn't attend signed up to mentor.
- Step 3
Count everyone who could be selected
The member is selected from those who signed up, so only mentors can be picked. The denominator must count mentors from both training groups, not all surveyed members. Add the two mentor counts:
- Step 4
Find the probability within the mentor group
Of the mentors, attended training. Type in Desmos. It displays ; use the fraction button to see . So the probability that a selected mentor attended training is . Grid in 21/31.