Binomial Distribution Exercises
J. Bridges Introduction to Statistics
1. You flip a coin 10 times. What is the probability of getting no heads in 10 tosses? Of
getting exactly 4 heads? Of getting 4 or more heads? Of getting less than 8 heads?
2. Ninety percent of the trees planted by a landscaping firm survive. What is the
probability that of the next 13 trees planted: a. at most ten will survive? b. at least ten
will survive? c. exactly ten will survive? That all of the trees will survive?
3. A machine produces parts of which 0.5% are defective. If a random sample of ten
parts produced by this machine contains more than one defective part, the machine is
shut down for repairs. Find the probability that the machine will be shut down for
repairs based on this sampling plan.
4. Assume that there are 600 “critical” parts in a car. “Critical” is defined as a part so
important that a failure will cause the car to be undrivable. Assume that each of these
critical parts has a 1 in 1,000 chance of failure during the first year of car ownership.
What is the overall probability that the car will be undrivable sometime during the first
year of ownership? If the failure probability for each part is 1 in 10,000, now what is the
overall probability?
5. According to an article in the February 1991 issue of Reader’s Digest, Americans face
a 1 in 20 chance of acquiring an infection while hospitalized. If the records of 15
randomly selected hospitalized patients are examined, find the probability that: a. at
least two develop an infection? b. none develop an infection?
6. Suppose that you take a five-question multiple-choice quiz by guessing. Each question
has possible answers a, b, c, d and only one is correct. (a) What is the probability that
you guess more than half of the answers correctly? (b) What is the probability that you
get all answers correct?
7. There is a 90% chance that Square Table Pizza will make a delivery in less than 30
minutes. An executive for Square Table decides to test the delivery system by ordering
20 pizzas at different times and different locations.
If the 90% rate is correct, find the probability that more than one pizza will be delivered
in 30 minutes or more.