Binomial, Geometric and Poisson Practice
KEY
Name __________________
1. It has been estimated that about 30% of frozen chicken contain enough salmonella
bacteria to cause illness if improperly cooked. A consumer purchases 12 frozen
chickens.
a. What is the probability that the consumer will have more than 6
contaminated chickens?
1- (Binompdf (12, .30, 0) + Binompdf (12, .30, 1) + …+ Binompdf (12, .30, 6)) = .0386
OR 1- binomcdf (12, .30, 6) = .0386
b. What is the probability that the consumer will have exactly 4 with
salmonella?
Binompdf (12, .3, 4) = .2311
2. Suppose 60% of a herd of cattle is infected with a particular disease. You have
125 cattle. How many do you expect to be infected? What is the standard deviation?
  np  125(.6)  75
 2  npq  126(.6)(.4)  30
  30  5.48
3. In playing a game of tossing a balanced die, if the number ‘3’ occurs, Bill will
win$50. If the number ‘6’ occurs, Bill will win $200. If the number ‘1’ or ‘2’ occurs,
Bill will lose $50. If the number ‘4’ or ‘5’ occurs, Bill will lose $100. Let X be the
amount of winning for Bill.
a. Write down the probability distribution of X, the amount of winning for Bill:
x
P(x)
$50
1/6
$200
1/6
-$50
1/3
-$100
1/3
b. If Bill continues to play he will either win or lose an amount. What do you expect,
on average, Bill will win per game? (Hint: expected value) E(x) = - $8.33
4. Light bulbs from batch A have a 10% chance of being damaged. You randomly
select light bulbs for testing.
a. What is the probability that the first damaged light bulb will be the fourth
one you choose?
geometpdf (.10, 4) = .0729
b. What is the probability that the first damaged light bulb will be the second
or third one you choose?
geometpdf (.10, 2) + geometpdf (.10, 3) = .171
c. What is the probability that the first damaged light bulb will be the 7th one
or after the 7th one?
x = 7, 8, 9, … so use the complement. 1 - geometcdf (.10, 6) = .5314
5. Tom is a field goal kicker. His success rate for field goals is 80%. Tom will kick
10 field goals. Let x, be the number of successful kicks.
a. Make a probability distribution for the 10 kicks
n = 10 p = .8
x
P(x)
0
0
1
0
2
0
3
.0007
4
.006
5
.0264
6
.088
7
.201
8
.302
9
.268
10
.107
b. Find the mean, variance and standard deviation  use L1, L2 or use the
formulas!
  np  10(.8)  8
 2  npq  10(.8)(.2)  1.6
  1.6  1.26
c. Find the probability of making exactly 1 field goal out of 10.
binompdf (10, .8, 1) = .000004
d. Find the probability of making at least 5 field goals out of 10.
P (at least 5) means x = 5, 6, 7, 8, 9 or 10 so we can use the complement.
1 - binomcdf (10, .8, 4) = .9936
Less than or equal to 4
6. My computer crashes on average 1.5 times a year. What is the probability of it
crashing exactly once this year?
Poissonpdf (1.5, 1) = .3347
7. The average classroom at BHS has 3.5 light bulbs burned out.
a. What is the probability of picking a classroom at random and it having 4
bulbs out?
Poissonpdf (3.5, 4) = .19
b. What is the probability of picking a classroom at random and it having
less than 4 bulbs out?
x = 0, 1, 2, 3
Poissoncdf (3.5, 3) = .537