Final answer:
The probability of exactly 2 successes in a binomial experiment with 15 trials and a success probability of 0.35 is calculated using the binomial probability formula. The values are plugged into the formula, and the result is then rounded to four decimal places to give the probability.
Step-by-step explanation:
To calculate the probability of exactly 2 successes in 15 independent trials of a binomial experiment with the success probability of 0.35, we use the binomial probability formula:
P(X = x) = (n choose x) × p^x × q^(n-x)
Where:
- n = number of trials
- x = number of successes to find the probability for
- p = probability of success on a single trial
- q = 1 - p = probability of failure on a single trial
In this case:
- n = 15
- x = 2
- p = 0.35
- q = 1 - 0.35 = 0.65
Now, we calculate the binomial coefficient (n choose x) for x = 2:
(15 choose 2) = 15! / (2! × (15-2)!) = 105
Substituting the values into the binomial probability formula, we get:
P(2) = 105 × 0.35^2 × 0.65^(15-2)
After calculating the above expression, we'll round the result to four decimal places as instructed. This is the probability of having exactly 2 successes in 15 trials when the success probability is 0.35.
the complete Question is given below:
A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n= 15, p = 0.35, x = 2 P(2)= ______
(Do not round until the final answer. Then round to four decimal places as needed.)