Selecting from bag/deck
Venn-diagrams and Two-way tables
Notation Pracitce
100
What is the probability of selecting a face card and then a red card from a deck of cards with replacement?
(12/52)(26/52)=312/2704 = 0.12 = 12%
100
If 74 students were surveyed on if they like Algebra and/or Geometry, what is the probability a student likes neither? 
74-43-6-5=20
20/74=0.27=27%
100
P(Ranch U doesn't like ketchup)?
40/62+14/62-8/62=46/62=0.74=74%
200
What is the probability of selecting two spades from a deck of cards without replacement?
(13/52)(12/51)=156/2652=0.06=6%
200
What is the probability the student is a sophomore and prefers vanilla? 
Must use overlap!! Do not multiply!
8/100 = 0.08 = 8%
(NOT 12/100*58/100 because it gives you 0.07 so the preference on ice cream flavor isn't independent of grade level).
200
P(doesn't like ranch | doesn't like ketchup)
6/14=0.43=43%
300
A bag contains 4 purple skittles, 5 yellow skittles, and 2 green skittles. What is the probability of selecting 3 green without replacement?
(2/11)(1/10)(0/9)=0/990=0=0%
300
What is the probability a student is a junior or likes swirl ice cream?
42-4-15 = 23 juniors like swirl ice cream.
P(junior) + P(swirl) - P(overlap)
42/100 + 62/100 - 23/100=81/100 = 0.81=81%
300
Find P(starbursts|skittles)
P(both)/P(skittles)
Skittles = 64+14 = 78 people
64/78=0.82=82%
400
What is the probability of selecting a king or a red face card from a standard deck of cards?
4/52+6/52-2/52=8/52=0.15=15%
400
If 74 students were surveyed on if they like algebra and/or geometry, what is the probability the student likes Geometry?
74-42-11-13=8
8+11 = 19 students like geometry
19/74=0.26=26%
400
Find P(starbursts)
# of people who like starbursts = 92 (28+64)
# of people total = 118 (28+64+14+12)
92/118 = 0.78 = 78%
500
A bag contains 4 purple skittles, 5 yellow skittles, and 2 green skittles. What is the probability of selecting a purple, then purple, then green with replacement?
(4/11)(4/11)(2/11)=32/1331=0.02=2%
500
In class, when asked about the best type of sour patch candy between sour patch kids, watermelon, BIG, and strawberry, 100 students voted. 40 of the students were juniors and the rest were sophomores. Of the students that voted, 1/20 students voted for BIG sour patch candy. 30 of the sophomores voted for watermelon and 7/20 of the juniors voted for watermelon. 3 Juniors voted for BIG, and 52.5% of the juniors voted for sour patch kids. Only 8 students voted for strawberry. Make a two-way table. 
500
Is liking starbursts depedent of liking skittles?
Use the venn diagram to make a two way table if you want to use ratios:
64:14 does not equal 28:12 OR
(92/118)(78/118)=0.515369
and
64/118=0.542372
So liking starbursts IS dependent on liking skittles (because it isn't independent).