Question

If a certain medicine cures 85% of the people who take it,what is the probability that, if 6 people take the medicine, exactly 4 will be cured?

Answer 1

The probability of exactly 4 people being cured out of 6 taking the medicine is 0.1762.

Step-by-step explanation:

We can use the binomial probability formula to calculate this probability. The formula is:

P(k successes in n trials) = (n choose k) * p^k * (1-p)^(n-k)

where:

n is the total number of trials (people taking the medicine in this case = 6)

k is the desired number of successes (cured people = 4)

p is the probability of success (cure rate = 85% = 0.85)

Plugging these values into the formula:

P(4 cured out of 6) = (6 choose 4) * 0.85^4 * 0.15^2

Calculating:

(6 choose 4) = 15 (combinations of choosing 4 out of 6)

0.85^4 ≈ 0.4259

0.15^2 = 0.0225

Therefore:

P(4 cured out of 6) = 15 * 0.4259 * 0.0225 ≈ 0.1762

Hence, the probability of exactly 4 people being cured out of 6 taking the medicine is approximately 0.1762.

Answer 2

if 6 people take the medicine, around 5 people will get cured if the cure probability is 85%.

Step-by-step explanation:

Given that a certain medicine cures 85% of the people who take it.

As 6 people take the medicine, we need to determine how many will be cured.

As

85% = 85/100 = 0.85

All we need is to multiply 6 with 0.85.

i.e. 6 × 0.85 = 5 (Rounded to the nearest 1 or the Ones Place)

Thus, if 6 people take the medicine, around 5 people will get cured if the cure probability is 85%.