# Effectiveness 80811

According to clinical studies, the effectiveness of the drug is 90%. The doctor prescribed the medicine to eight patients. What is the probability that the drug will be effective in all these patients?

### Correct answer:

**Showing 1 comment:**

**Math student**

The effectiveness of the drug is 90% or 0.9, which means that the probability of the drug being effective for any given patient is p = 0.9. We can use the binomial distribution to calculate the probability of the drug being effective in all eight patients, assuming that each patient is independent.

Let X be the number of patients for whom the drug is effective. The number of trials is n = 8, and the probability of success is p = 0.9. The probability of getting exactly k successes out of n trials is given by the binomial distribution formula:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where (n choose k) is the number of ways to choose k successes out of n trials, which is given by the binomial coefficient.

To find the probability of the drug being effective in all eight patients, we need to calculate the probability of getting exactly eight successes:

P(X = 8) = (8 choose 8) * 0.9

= 0.9

= 0.43046721

Therefore, the probability of the drug being effective in all eight patients is approximately 0.4305 or 43.05%. This means that there is a 43.05% chance that all eight patients will respond to the drug and have positive outcomes.

Let X be the number of patients for whom the drug is effective. The number of trials is n = 8, and the probability of success is p = 0.9. The probability of getting exactly k successes out of n trials is given by the binomial distribution formula:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where (n choose k) is the number of ways to choose k successes out of n trials, which is given by the binomial coefficient.

To find the probability of the drug being effective in all eight patients, we need to calculate the probability of getting exactly eight successes:

P(X = 8) = (8 choose 8) * 0.9

^{8}* (1-0.9)^(8-8)= 0.9

^{8}= 0.43046721

Therefore, the probability of the drug being effective in all eight patients is approximately 0.4305 or 43.05%. This means that there is a 43.05% chance that all eight patients will respond to the drug and have positive outcomes.

Tips for related online calculators

Looking for a statistical calculator?

Our percentage calculator will help you quickly calculate various typical tasks with percentages.

Would you like to compute the count of combinations?

Our percentage calculator will help you quickly calculate various typical tasks with percentages.

Would you like to compute the count of combinations?

#### You need to know the following knowledge to solve this word math problem:

## Related math problems and questions:

- Successfully 19843

The drug successfully treats the disease in 96% of cases. Your doctor will treat 50 patients with this medicine. What number of cures is most likely? - Medicine

We test medicine on six patients. For all, the drug doesn't work. If the drug success rate of 20%, what is the probability that medicine does not work? - Doctors

The drug successfully treats 90% of cases. Calculate the probability that it will cure at least 18 patients out of 20. - Probability 30271

The probability of an adverse drug reaction is 2.1%. How many people need to be prescribed for one patient to experience side effects with a chance of 90%? - Brakes of a car

For the brakes of a passenger car to be effective, it is prescribed that a car be moving on a horizontal road at a speed of 40 km. A car must stop on the track 15.4 m. What is the deceleration of the car? - Containers

One in eight containers is temporarily misplaced. A random sample of 12 containers is selected. What is the probability that 6 of these containers will be temporarily misplaced? - Non-conforming 19863

The probability that a quality product will meet all technical requirements is 0.95. What is the probability that all three randomly produced products will be: a) conforming, b) non-conforming - Doctor 2

A doctor noted the Diastolic Blood Pressure (DBP) of a large number of patients. Later, he scrambled the data to keep the privacy of his patients. Based on the scrambled dataset, he finds that the lower inner fence is equal to 50 and the upper inner fence - Two doctors

Doctor A will determine the correct diagnosis with a probability of 89% and doctor B with a probability of 75%. Calculate the probability of proper diagnosis if both doctors diagnose the patient. - Win in raffle

The raffle tickets were sold to 200, 5 of which were winning. What is the probability that Peter, who bought one ticket, will win? - Probability 3322

We have the numbers 4, 6, 8, 10, and 12. What is the probability that with a randomly selected triangle, these will be the lengths of the sides of a scalene triangle? - Mastering

The student masters the subject matter for the exam in Czech to 98%, from Math to 86%, and from Economics to 71%. What is the probability that he will fail in Math and that others will succeed? - Population variance

In a California community college, 60% of students will transfer to a college in the CSU system. The number of students in a sample who will transfer follows a binomial distribution. If eight students are randomly selected, find the population variance σ² - Fertilizer 80787

The fertilizer contains 15.8% nitrogen. Calculate the mass of fertilizer that must be added to the soil to make 17.0 g of nitrogen effective. Addition losses are 6.60%. - Seeds

The germination of seeds of a certain species of carrot is 96%. What is the probability that at least 25 seeds out of 30 will germinate? - Suppose 4

Suppose that 14% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote the number among these that are nonconforming and can be - One-quarter 6369

According to research, one-quarter of pupils will encounter drugs at the end of primary school. Of this number, 40% of pupils try the drug. How many students attend Year 9 if 12 have signed up to use drugs?