Download Math 309 Supplemental Problems – Discrete Random

Math 309 Supplemental Problems – Discrete Random Variables
If any of these problems involve special distributions that we have studied – name that distribution.
1. The probability that a patient recovers from a delicate heart operation is 0.9. What is the probability that exactly
five of the next seven patients having this operation survive? Let X = {the number of patients of these 7 patients
who survive}. Give the probability function for X.
2. A box has 3 red balls, 5 blue balls, and 2 green balls. You draw a ball. If it is not red, you return the ball and
draw again. What is the probability that the first red ball is on the 3rd draw? the 7th draw? the nth draw?
3. A cookie jar has 4 chocolate chip cookies and 3 vanilla cookies. You randomly select (and eat) two cookies.
What is the probability that you eat exactly one chocolate chip cookie?
4. It is known that 45% of mice inoculated with a serum are protected from a certain disease. If 5 mice are
inoculated, find the probability that:
a) none contracts the disease;
b) fewer than 2 contract the disease;
c) more than 3 contract the disease.
5. Jim has a batting average of .285. What is the probability that he gets exactly 3 hits in his next 10 bats? Let H =
{the number of hits that Jim gets in his next 10 bats}. Give the probability function for H.
6. In a certain manufacturing process it is known that, on average, 1 in every 100 items is defective. What is the
probability that the fifth random item inspected is the first defective item found?
7. An oil prospector will drill a succession of holes to find a productive well. The probability of that he hits oil on a
given hole is 0.2. Assume that the probability of hitting oil on one hole is independent of hitting it on another.
What is the probability that his first productive well is found on the tenth hole?
8. You roll three dice successively until you get a six on all three dice. Let X = {the number of rolls of the 3 dice}.
Find the probability mass function for X. What is the probability that you roll the dice 100 times?
9. You randomly select 6 light bulbs from a box that contains 7 good and 3 defective bulbs. What is the probability
that you selected exactly two defective bulbs? What is the probability that you select at least 2 defective bulbs?
(Note that you are not replacing the bulbs between selections.)