Here, you get to practice finding binomial probabilities by using a formula. The following problems have a binomial random variable with p = 0.55. Use the following formulas for the binomial distribution for the problems.
where
and
n! = (n – 1)(n – 2)(n – 3) . . . (3)(2)(1)
Sample questions
What is the probability of exactly one success in eight trials? Round your answer to four decimal places.
Answer: 0.0164
The formula for calculating a probability for a binomial distribution is
Here,
and n! means n(n – 1)(n – 2) . . . (3)(2)(1). For example 5! = (5)(4)(3)(2)(1) = 120; 2! = (2)(1) = 2; 1! = 1; and by convention, 0! = 1.
To find the probability of exactly one success in eight trials, you need P(X = 1), where n = 8 (remember that p = 0.55 here):
Rounded to four decimal places, the answer is 0.0164.
What is the probability of exactly two successes in eight trials? Round your answer to four decimal places.
Answer: 0.0703
The formula for calculating a probability for a binomial distribution is
Here,
and n! means n(n – 1)(n – 2) . . . (3)(2)(1). For example 5! = (5)(4)(3)(2)(1) = 120; 2! = (2)(1) = 2; 1! = 1; and by convention, 0! = 1.
To find the probability of exactly two successes in eight trials, you want P(X = 2), where n = 8 (remember that p = 0.55 here):
Rounded to four decimal places, the answer is 0.0703.
What is the probability of getting at least one success in eight trials? Round your answer to four decimal places.
Answer: 0.9983
The formula for calculating a probability for a binomial distribution is
Here,
and n! means n(n – 1)(n – 2) . . . (3)(2)(1). For example 5! = (5)(4)(3)(2)(1) = 120; 2! = (2)(1) = 2; 1! = 1; and by convention, 0! = 1.
In this case, X is the number of successes in n trials. You want
because "at least one" means the same as "one or more." The easiest way to answer this question is to take 1 minus P(X = 0), because that's the opposite and easier to find.
Rounded to four decimal places, this answer is 0.017. Now, plug the value of P(X = 0) in the formula to find P(X > 0):
If you need more practice on this and other topics from your statistics course, visit 1,001 Statistics Practice Problems For Dummies to purchase online access to 1,001 statistics practice problems! We can help you track your performance, see where you need to study, and create customized problem sets to master your stats skills.
