Algebra II : Using Probability to Make Decisions
Study concepts, example questions & explanations for Algebra II
All Algebra II Resources
Example Questions
Example Question #11 : Using Probability To Make Decisions
Ann, Bob and Cathy are students working together on a group project for school. The project involves three tasks, each of which one of the three students will complete: creating a model, interviewing a local expert, and writing a report. No student has the time to complete more than one task, and all three of them have a strong preference for interviewing the local expert. They decide to randomly distribute the three tasks among themselves in a fair manner, such that all three of them have equal odds of completing their preferred task.
After some consideration, they reach for a coin. Bob flips it; if it lands heads, he creates the model; if tails, he interviews a local expert. After he is assigned a task by this method, Cathy flips a coin. If it lands heads, she writes the report; if tails, she is assigned the other remaining task. Ann is then assigned whichever task is left. By this method, the group decides that Bob will create the model, Cathy will interview the local expert and Ann will write the report.
Was their chosen method fair?
No. Bob had a higher probability of interviewing the local expert than Ann or Cathy did.
No. Ann never flipped the coin, so she never had an opportunity to obtain a coin result that would assign her to interview the local expert.
Yes. Coins have equal odds of landing on heads or tails, so flipping a coin is a fair way to make a decision between options.
Yes. All three students have equal probabilities of interviewing the expert.
No. Bob had a higher probability of interviewing the local expert than Ann or Cathy did.
Bob’s coin flip gives him a 50% chance of obtaining each of the two tasks assigned to his coin flip (creating the model or interviewing the local expert), so he has a 50% chance of interviewing the local expert. The total probability that the task will be assigned to one of the three of them is 1. Ann and Cathy both have a nonzero chance of interviewing the local expert; for instance, if Bob and Cathy both land heads, Ann would be assigned her preferred task. The following relationships express this:
Ann’s probability + Bob’s probability + Cathy’s probability = 1
A + B + C = 1
A + 0.5 + C = 1
A + C = 0.5
C > 0
A > 0
Therefore, both C and A must be less than 0.5, so Bob’s probability of completing his preferred task is higher than both Cathy’s and Ann’s probabilities.
Example Question #12 : Using Probability To Make Decisions
Ann, Bob and Cathy are students working together on a group project for school. The project involves three tasks, each of which one of the three students will complete: creating a model, interviewing a local expert, and writing a report. No student has the time to complete more than one task, and all three of them have a strong preference for interviewing the local expert. They decide to randomly distribute the three tasks among themselves in a fair manner, such that all three of them have equal odds of completing their preferred task.
After some consideration, they reach for a coin. Bob flips it; if it lands heads, he creates the model; if tails, he interviews a local expert. After he is assigned a task by this method, Cathy flips a coin. If it lands heads, she writes the report; if tails, she is assigned the other remaining task. Ann is then assigned whichever task is left.
What is the probability that Ann is assigned to interview the expert?
0.25 or 25%
1.0 or 100%
Cannot be determined
0.50 or 50%
0.25 or 25%
Ann’s probability of interviewing the expert is reliant on two events: Bob’s coin toss and Cathy’s coin toss. For Ann to interview the expert, Bob must flip heads and Cathy must then flip heads as well. Each coin toss has a 50% odds of any one outcome, so Ann’s probability of interviewing the expert may be calculated as follows:
Event 1 * Event 2 = Ann’s probability
0.5 * 0.5 = 0.25
Therefore, Ann’s probability of interviewing the expert is 0.25, or 25%. Note that this method of allocating tasks is therefore not fair, as the three students will not have equal probabilities of interviewing the expert.
All Algebra II Resources
