Data Unit 4 Test Flashcards
S
Universal Set (this represents everybody) Written in the top left corner
Write leftovers in the bottom right corner of the
Venn diagram
Always draw a rectangle around the
Venn diagram
When calculating the total of a venn diagram
add all the numbers together
When calculating the number of students in a specific class,
add all numbers in a circle
n =
number
Where U is “the
union of” (or the word “or” is used > implies addition)
Where ∩ “the
intersection of” (or the word “and” is used > implies multiplication)
Principle of Inclusion & Exclusion for 2 Sets Formula:
n(A U B) = n(A) + n(B) - n(A ∩ B)
At least one in Venn Digrams -
One option, the other option, or both options
When using Venn DIagrams, ALWAYS START WITH THE
OVERLAP
At least
Union U
More than one =
Add up all the overlaps - with a Venn diagram it can’t be taken straight from the data or students will be counted twice
Principle of Inclusion & Exclusion for 3 Sets Formula:
n(C U F U D) = n(C) + n(F) + n(D) - n(C∩F) - (C∩D) - n(F∩D) + n(C∩F∩D)
- Overlaps are subtracted and added back in
Order is
not important
It is just the combination of things,
not in any specific order
Combination formula
C( n , r ) = n! /( n - r )! r!
-It is the permutation formula divided by duplicates (removing order, dividing out the permutations)
Ex. Evaluate a) (10,2) b) C(10,8)
45 and 45 are the answers - You can pick 8 for a committee and leave 2 behind in the same # of ways
Same options for selecting r and not selecting r.
Ex. 1
In how many ways can 4 cards be dealt from a regular deck of 52 playing cards if:
a) No restrictions
“52 choose 4” C(52,4) = 270,725
Ex. 1
In how many ways can 4 cards be dealt from a regular deck of 52 playing cards if:
b) One card must be the ace of spades
Ace: C(1,1) Spades: C(51,3) = 20825
1 + 51 = 52, 1 + 3 = 4
Ex. 1
In how many ways can 4 cards be dealt from a regular deck of 52 playing cards if:
c) Exactly one card must be a 2
2’s: C(4,1) Not 2: C(48,3) = 69184
52 = 4 + 48, 4 = 1 + 3
Ex. 1
In how many ways can 4 cards be dealt from a regular deck of 52 playing cards if:
d) At least one card must be a 2
Direct
C(4,1) C(48,3) + C(4,2) C(48,2) + C(4,3) C(48,1) + C(4,4) C(48,0)
one 2 two 2’s three 2’s four 2’s
= 4(17296) + 6(128) + 9(48) + 1(1)
= 69184 + 6768 + 192 + 1
= 76145
Indirect
All possible outcomes - no 2’s
C(52,4) - C(48,4) = 270725 - 194580
= 76145