Participants in a study of a new medication received either medication A or a placebo. Find P(placebo and improvement). You may find it helpful to make a tree diagram of the problem on a separate piece of paper.
Of all those who participated in the study, 80% received medication A.
Of those who received medication A, 76% reported an improvement.
Of those who received the placebo, 62% reported no improvement.
I don't know how to do this at all, any hints or help would be nice. :)
Thanks for this! Remember, it's not cheating unless you're caught.
participants—80% Medication A-----76% improvement
24% no improvement
20% placebo-------38% improvement
62% no improvement
20%*38%=.2*.38-7.6%
Well, let's break it down step by step and have some fun along the way!
First, we know that 80% of the participants received medication A. So let's imagine we have a group of 100 people. That means 80 people received medication A, and the remaining 20 people received the placebo.
Now, let's focus on the group that received medication A. Out of those 80 people, 76% reported an improvement. So, how many people would that be? Let's calculate that using my clown math skills.
76% of 80 people is (80 * 76)/100 = 60.8 people. Well, we can't have 0.8 of a person, so let's round it to 61 people.
Next, let's consider the group that received the placebo. We know that 62% of them reported no improvement. So, how many people would that be? Brace yourself, it's time for more clown math!
62% of 20 people is (20 * 62)/100 = 12.4 people. Again, we can't have 0.4 of a person, so let's round it to 12 people.
Now, we want to find the probability of someone receiving the placebo and reporting an improvement. We have 12 people who received the placebo, but 12 out of how many?
In total, we had 100 participants—80 who received medication A and 20 who received the placebo. So, the probability is 12/100 = 0.12, or 12%.
So, the probability of someone receiving the placebo and reporting an improvement is 12%. And that's the way the clown cookie crumbles!
To find the probability of receiving a placebo and reporting an improvement, we can break down the problem step by step.
Step 1: Draw a tree diagram
To visually represent the problem, draw a tree diagram. Start by labeling the branches with the possible outcomes: Medication A or Placebo. Then, on each branch, add another level to represent the improvement or no improvement reported.
_______Medication A_______
/ \
Improvement No Improvement
(76% reported) (24% reported)
_______Placebo________
/ \
Improvement No Improvement
(??%) (62% reported)
Step 2: Calculate the missing probability
We know that 80% received Medication A, which means the remaining 20% received the Placebo. Since the sum of probabilities of all possibilities in an event is equal to 1, we can deduce that the probability of receiving the Placebo is 20%.
So, the probabilities for the branches of the Placebo can be filled in as:
_____Placebo(20%)_____
/ \
Improvement No Improvement
(??%) (62% reported)
Step 3: Calculate the missing probability for improvement
To find the probability of improvement for the Placebo branch, we can subtract the probability of no improvement from 100% since the total probability for the branch should add up to 100%.
Therefore, the probability of improvement for the Placebo branch is:
100% - 62% = 38%
Now the tree diagram looks like this:
_______Medication A_______
/ \
Improvement No Improvement
(76% reported) (24% reported)
_______Placebo________
/ \
Improvement No Improvement
(38%) (62% reported)
Step 4: Find the desired probability
From the tree diagram, we can see that the probability of receiving the Placebo and reporting an improvement is 38%.
So, P(placebo and improvement) = 38%.
Conclusion:
Using the probabilities and the tree diagram, we calculated that the probability of receiving a placebo and reporting an improvement is 38%.