Problemas
The Hiking Club plans to go camping in a State park where the probability of rain on any given day is 1/4 . What is the probability that it will rain on exactly one of the five days they are there?Round your answer to the nearest thousandth.
Roztwór
Ramona
professionell · Tutor durante 6 años
4.1
(239 Votos)
Respuesta
To solve this problem, we can use the binomial probability formula. The binomial probability formula is used to find the probability of obtaining a fixed number of successes in a fixed number of independent Bernoulli trials.The binomial probability formula is given by:P(X = k) = (n choose k) * p^k * (1-p)^(n-k)Where:- P(X = k) is the probability of obtaining k successes in n trials- n is the number of trials- k is the number of successes- p is the probability of success in a single trial- (1-p) is the probability of failure in a single trialIn this case, the Hiking Club plans to go camping in park of rain on any given day is 1/4. We want to find the probability that it will rain on exactly one of the five days they are there.Given information:- Probability of rain on any given day (p) = 1/4- Number of days they are there (n) = 5- Number of days it will rain (k) = 1Plugging these values into the binomial probability formula:P(X = 1) = (5 choose 1) * (1/4)^1 * (3/4)^(5-1)P(X = 1) = 5 * (1/4) * (3/4)^4P(X = 1) = 5 * (1/4) * (81/256)P(X = 1) = 5 * (1/4) * (81/256)P(X = 1) = 5 * (81/1024)P(X = 1) = 405/1024P(X = 1) ≈ 0.396Therefore, the probability that it will rain on exactly one of the five days they are there is approximately 0.396, rounded to the nearest thousandth.