help me with this. Please get it right....
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.
P(X=16)
, n=17
, p=0.6
To find P(X = 16) with n = 17 and p = 0.6, we use the formula for the probability mass function of a binomial distribution:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
where (n choose k) is the number of ways to choose k successes out of n trials.
Plugging in the values n = 17, p = 0.6, and k = 16 into the formula:
P(X = 16) = (17 choose 16) * (0.6)^16 * (0.4)^(17-16)
P(X = 16) = 17! / (16! * 1!) * (0.6)^16 * 0.4
P(X = 16) = 17 * 0.6^16 * 0.4
P(X = 16) = 0.0057
Therefore, the probability of obtaining exactly 16 successes out of 17 trials with a probability of success of 0.6 is approximately 0.0057 when rounded to four decimal places.