Respuesta :
This is a binomial distribution problem, so lest first identify the probabilty on "winning" and "losing":
It is said that 0.4 recovers, so 0.6 will not recover.
Now we are going to multiply the probabilities using the given information:
[tex]P(x=5)=\frac{15!}{10!5!}\cdot0.4^5\cdot0.6^{10}[/tex]The first part represents the number of combinations of 5 people in a group of 15, the second one the probability that exactly 5 of them will recover and the last part the probability for those that will not recover.
[tex]P(x=5)\approx0.1859[/tex]This is the probability that exactly 5 will recover, but as the problem says that at most 5 people will survive, we could do the same for 4, 3, 2, 1 and 0.
By doing so and adding the probabilities we get:
[tex]P(x\le5)\approx0.4032[/tex]That is the probability that at most 5 people will survive.
