If a treatment is effective in 80% of cases, what is the probability that it wil

If a treatment is effective in 80% of cases, what is the probability that it will be effective for at least one out of three patients? (2023)

If a treatment is effective in 80% of cases, what is the probability that it will be effective for at least one out of three patients? (2023)

Step 1: Understand that the treatment is effective in 80% of cases. This means the probability of it being effective for one patient is 0.8.
Step 2: Calculate the probability that the treatment is NOT effective for one patient. This is 1 - 0.8 = 0.2.
Step 3: Since we are looking at three patients, we need to find the probability that the treatment is NOT effective for all three patients. This is calculated as 0.2 (not effective for one patient) raised to the power of 3 (for three patients), which is 0.2^3 = 0.008.
Step 4: Now, to find the probability that the treatment is effective for at least one out of the three patients, we subtract the probability that it is not effective for all three from 1. This is 1 - 0.008 = 0.992.
Step 5: Therefore, the probability that the treatment will be effective for at least one out of three patients is 0.992.

Probability of Complement Events – Understanding how to calculate the probability of at least one success by using the complement rule.
Independent Events – Recognizing that the effectiveness of the treatment for each patient is independent of the others.