Final answer:
To find the probability of successful treatment in two out of five cases, we can use the binomial probability formula. The probability of successful treatment in two out of five cases is 0.2304, or 23.04%.
Step-by-step explanation:
To find the probability of successful treatment in two out of five cases, we can use the binomial probability formula.
The binomial probability formula is given by:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
- P(X = k) is the probability of getting exactly k successful treatments
- C(n, k) is the number of combinations of n treatments taken k at a time
- p is the probability of one treatment being successful (in this case, 0.6)
- n is the total number of treatments (in this case, 5)
- k is the number of successful treatments we want (in this case, 2)
Plugging in the values, we get:
P(X = 2) = C(5, 2) * (0.6)^2 * (1-0.6)^(5-2)
P(X = 2) = 10 * 0.36 * 0.064
P(X = 2) = 0.2304
Therefore, the probability of successful treatment in two out of five cases is 0.2304, or 23.04%.