Question

# A clinic offers an experimental treatment to patients with a certain disease. It is known that the 30% of patients who receive treatment experience significant improvement. However, It is also observed that 20% of patients who do not receive treatment improve. Yes in the end From the study it is observed that 60% of the patients who improved received the treatment, what is the probability that a patient who received the treatment will experience improvement significant?

271

likes
1353 views

## Answer to a math question A clinic offers an experimental treatment to patients with a certain disease. It is known that the 30% of patients who receive treatment experience significant improvement. However, It is also observed that 20% of patients who do not receive treatment improve. Yes in the end From the study it is observed that 60% of the patients who improved received the treatment, what is the probability that a patient who received the treatment will experience improvement significant?

Santino
4.5
To solve this problem, we can use Bayes' theorem and organize the information given into probabilities:

- Let T be the event that a patient receives the treatment.
- Let I be the event that a patient experiences significant improvement.

From the problem statement, we have:
- P$I|T$ = 0.30
- P$I|T^c$ = 0.20
- P$T|I$ = 0.60

We need to find P$T|I$ , the probability that a patient received treatment given that they improved.

Using Bayes' theorem, we can rewrite P$T|I$ as:
P$T|I$ = \frac{P$I|T$P$T$}{P$I$}

Let's find P$I$ using the law of total probability:
P$I$ = P$I|T$P$T$ + P$I|T^c$P$T^c$

Assume the proportion of patients who received treatment is p , then:
P$T$ = p \quad \text{and} \quad P$T^c$ = 1 - p

Substitute these into the equation:
P$I$ = 0.30p + 0.20$1 - p$

Solve for p using the equation 0.60 = \frac{0.30p}{0.10p + 0.20} . The solution for p is 0.5, meaning that 50% of the patients received treatment.

Now, find P$I$ :
P$I$ = 0.10p + 0.20 = 0.10$0.5$ + 0.20 = 0.25

Finally, the probability that a patient who received the treatment will experience significant improvement is P$I|T$ = 0.30 .

Therefore, the probability that a patient who received the treatment will experience significant improvement is **30%**.

\boxed{P$I|T$ = 0.30}

Frequently asked questions $FAQs$
Question: Find the basis of vectors in R^3 for the subspace spanned by {$1, 2, 3$, $-1, 0, 2$, $3, 4, 5$}.
+
Math question: Convert 3.6 x 10^4 to standard form.
+
Question: Given a circle with radius 6 units, what is the area, in square units, of a rectangle inscribed inside it?
+