Question

When treated with an​ antibiotic, 93​% of all the dolphins are cured of a particular bacterial infection. If 6 dolphins with the particular bacterial infection are​ treated, find the probability that exactly 3 are cured.

Answer 1

The probability that exactly 3 out of 6 dolphins are cured when treated with an antibiotic is approximately 0.4108 or 41.08%.

Step-by-step explanation:

To find the probability that exactly 3 out of 6 dolphins are cured when treated with an antibiotic, we can use the binomial probability formula:

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

In this case, n = 6 (number of dolphins treated), k = 3 (number of dolphins cured), and p = 0.93 (probability of a dolphin being cured). Substituting these values into the formula:

P(X = 3) = 6C3 * 0.93^3 * (1 - 0.93)^(6 - 3)

Simplifying:

P(X = 3) = 20 * 0.93^3 * (0.07)^3

P(X = 3) ≈ 0.4108

The probability that exactly 3 out of 6 dolphins are cured is approximately 0.4108 or 41.08%.

Answer 2

the probability is 0.00552

Step-by-step explanation:

If 93% are cured, the percentage not cured will be 100-93 = 7%

let p = probability of being cured = 93% = 93/100 = 0.93

q = probability of being uncured = 7/100 = 0.07

so we proceed to use the bernoulli approach;

we have this as;

P(X = n) = X C n p^n q^n-1

P(X = 3) = 6 C 3 * 0.93^3 * 0.07^3

P(X = 3) = 0.00552