MidTerm

Question 1

P( A or B ) =

Answer 1

P( A or B ) = P( A ) + P( B ) - P( A and B )

Question 2

P( A or B or C ) =

Answer 2

P( A or B or C ) = P( A ) + P( Ac and B ) + P( Ac and Bc and C )

Question 3

| equals what 2 equations?

y - x | > .3

Answer 3

y > x + .3 and y < x - .3

Question 4

Set A = area(A)
Uni Set = area(Uni)
what is the probability of set A?

Answer 4

area(A)/area(Uni)

Question 5

when calculating continuous probabilities we use _____ instead of ______

Answer 5

area instead of # of elements

Question 6

when calculating discrete probabilities we use _____ instead of ______

Answer 6

of elements instead of area

Question 7

P( A | B ) = ?

Answer 7

P( A | B ) = P( A and B ) / P( B )

Question 8

P( A & B ) = ?

Answer 8

P( A and B ) = P( B ) * P( A | B )

Question 9

P( Bc | A ) = ? (if B and Bc are all possibilities)

Answer 9

P( Bc | A ) = 1 - P( B | A )

Question 10

P( A1 & A2 & A3) = ?

Answer 10

P( A1 and A2 and A3 ) = P(A1) * P( A2 | A1 ) * P( A3 | A1&A2 )

Question 11

How many decisions (depth) would a tree have with P( A1 & A2 & A3 & A4)

Answer 11

4 deep

Question 12

Best way to do multiplication rule? When a question asks you for P( A & B & C )

Answer 12

use a decision tree and map out
P( A ) * P( B | A) * P( C | A&B )
br1 * br2 * br3

Question 13

Total Probability Theorem

P( B ) = ?

Answer 13

Assume A1, A2, A3 …. An are disjoint and are added up to equal the universal set then
P( B ) = P( A1 ) * P( B | A1) +P( A2 ) * P( B | A2 ) + P( A3 ) * P( B | A3 ) ….. + P( An ) * P( B | An)

Question 14

multiplication rule

Answer 14

P( A1 & A2 & A3 ) = P( A1 ) * P( A2 | A1 ) * P( A3 | A1 & A2 )

Question 15

total probability rule formula

Answer 15

P( B ) = P( A1 & B ) + P( A2 & B ) + … + P( An & B )
which turns into
P( B ) = P( A1 ) * P( B | A1 ) + P( A2 ) * P( B | A2 ) + … + P( An ) * P( B | An )

Question 16

Baye’s Law

Answer 16

P( Ai | B ) = [ P( Ai ) * P( B | Ai ) ] / P( B )
and
P( B ) = P( A1 ) * P( B | A1 ) + P( A2 ) * P( B | A2 ) + … + P( An ) * P( B | An )

Question 17

Given P( B | A ) and we want to find P( A | B ) what should we use?

Answer 17

Baye’s Law

P( Ai | B ) = [ P( Ai ) * P( B | Ai ) ] / P( B )

Question 18

First step in reading a probability probem

Answer 18

IDENTIFY THE GIVENS

Question 19

If we know A & B are independent sets:
P( A & B ) = ?
P( A | B ) = ?
P( B | A ) = ?

Answer 19

P( A & B ) = P( A ) * P( B )
P( A | B ) = P ( A )
P( B | A ) = P ( B )

Question 20

Binomial Probability (if we care about order)

Answer 20

where p is probability of first outcome (Heads) and 1-p is probability of second outcome (Tails) and n is the number of trials and k is the desired number of first outcome desired.
P(k) = p^k * (1-p) ^(n-k)

Question 21

Binomial Probability (if we don’t care about order)

Answer 21

( n choose k ) p^k (1-p)^(n-k)

Question 22

(n choose k) = ?

Answer 22

n! / k! (n-k)!

Question 23

How many combinations can we have with n distinct letters?

Answer 23

n!

Question 24

How many combinations can we have with n distinct letters and we pick k without replacement?>

Answer 24

n! / ( n-k )!

Question 25

If we have multiple repeating letters and a total number of letters = t then how do we calc? x y z are the repeating lettters.

Answer 25

t! / #ofx! #ofy! #ofz!

Question 26

total number of objects = t
total number of objects is partitioned into 3 categories. p1 p2 and p3 (represent the number need for each partition)
how many combinations?

Answer 26

t! / p1! p2! p3!

Question 27

how to calculate combinations? n total items pick k

Answer 27

n! / k! ( n-k )!