APMA 3100 Exam
1Question and
answers rated A+
2025/2026
1. P[A *B] if A and B are P[A] + P[B] - P[A )B]
depen-dent
2. P[A|B] ("A given B") P[A )B] / P[B] =
( [B | A] * P[A] ) / P[B]
3. Law of Total Probability If two sets, A and A^C, form a partition, and B intersects
those
sets, then P [B] = P[B )A] + P[B )A^C]
4. How can you tell if A and B are If P[A] * P[B] = P[A )B]
independent?
5. Fundamental Counting Princi- If an experiment has m possible outcomes, and a
second ex-
ple periment has n possible outcomes, the total possible
outcomes is given by m * n
6. How many ways are there
n!
to order n objects?
7. How many possible outcomes n! / (n-k)! (Permutation)
are there to order k
objects from n objects
where order matters?
8. How many possible outcomes n! / k!(n-k)!
are there to order k objects
from n objects where we
don't want to count different
order of same objects?
9. If an experiment is repeated n (n choose k) * p^k * (1-p)^(n-k)
times and has a probability p
1/
5
, APMA 3100 Exam 1
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of success, what is the
proba-bility of k successes?
10. Multinomial Probability Law If an experiment is repeated a finite n times, and you're
trying
to calculate probability of P[G = x, R = y, Q = z], then
probability
= n! / (x! y! z!) * P[G]^x * P[R]^y * P[Q]^z
11. for events A and B P[A *B] =1 - P[A^C B ^C]
12. Rules of a probability
mass function 1. PX(x) >= 0 for each x
2. Sum of all probabilities must equal 1
3. Graphed as "bar graph"
13. Rules of a cumulative distribu- 1. PX[x < 0] = 0
tion 2. Gaps between steps tell P[X=x] (as opposed to
P[X <= x])
function
3. Graphed as "step graph"
14. Expected Value Formula E = [x * P(x)]
15. E[X^2] X^2 * P[X]
16. Var[X] E[X^2] - (E[X])^2
17. Distinction between X and x X is the random variable: a number assigned to each
outcome
x is the graphical x: the independent variable
18. When would you use a 20. When would you use a Geo-metric
Bernoulli random random variable?
variable?
19. When would you use a
Bino-mial random
variable?
2/
5
1Question and
answers rated A+
2025/2026
1. P[A *B] if A and B are P[A] + P[B] - P[A )B]
depen-dent
2. P[A|B] ("A given B") P[A )B] / P[B] =
( [B | A] * P[A] ) / P[B]
3. Law of Total Probability If two sets, A and A^C, form a partition, and B intersects
those
sets, then P [B] = P[B )A] + P[B )A^C]
4. How can you tell if A and B are If P[A] * P[B] = P[A )B]
independent?
5. Fundamental Counting Princi- If an experiment has m possible outcomes, and a
second ex-
ple periment has n possible outcomes, the total possible
outcomes is given by m * n
6. How many ways are there
n!
to order n objects?
7. How many possible outcomes n! / (n-k)! (Permutation)
are there to order k
objects from n objects
where order matters?
8. How many possible outcomes n! / k!(n-k)!
are there to order k objects
from n objects where we
don't want to count different
order of same objects?
9. If an experiment is repeated n (n choose k) * p^k * (1-p)^(n-k)
times and has a probability p
1/
5
, APMA 3100 Exam 1
Study online at https://quizlet.com/_csw4rm
of success, what is the
proba-bility of k successes?
10. Multinomial Probability Law If an experiment is repeated a finite n times, and you're
trying
to calculate probability of P[G = x, R = y, Q = z], then
probability
= n! / (x! y! z!) * P[G]^x * P[R]^y * P[Q]^z
11. for events A and B P[A *B] =1 - P[A^C B ^C]
12. Rules of a probability
mass function 1. PX(x) >= 0 for each x
2. Sum of all probabilities must equal 1
3. Graphed as "bar graph"
13. Rules of a cumulative distribu- 1. PX[x < 0] = 0
tion 2. Gaps between steps tell P[X=x] (as opposed to
P[X <= x])
function
3. Graphed as "step graph"
14. Expected Value Formula E = [x * P(x)]
15. E[X^2] X^2 * P[X]
16. Var[X] E[X^2] - (E[X])^2
17. Distinction between X and x X is the random variable: a number assigned to each
outcome
x is the graphical x: the independent variable
18. When would you use a 20. When would you use a Geo-metric
Bernoulli random random variable?
variable?
19. When would you use a
Bino-mial random
variable?
2/
5
