Union, Intersection
Intersection of Sets
3
Intersection of Sets
• Intersection (∩) [of 2 sets]: the elements common to both sets
• Some guidelines when finding the intersection of 2 sets:– Usually easier to start with the set containing
the least number of elements
4
Solving Compound Inequalities Using Intersection
• Can be found in two formats:– Two linear inequalities separated by the word and
– A statement containing two inequality symbols• -4 < x < 7
Union of Sets
6
Union of Sets
• Union (U) [of 2 sets]: the combination of the distinct elements from both sets
• Some guidelines when finding the union of 2 sets:– “Dump” the elements of both sets together
and remove the duplicates
1
2
1
51 1 1
2 5 10
S
T
R
O
P1
2
3
6
5
4
Example: Suppose you spin each of these two spinners. What is the probability of spinning an even number and a vowel?
P(even) = (3 evens out of 6 outcomes)
(1 vowel out of 5 outcomes)P(vowel) =
P(even, vowel) =
Independent Events
Slide 7
Dependent Event
• What happens the during the second event depends upon what happened before.
• In other words, the result of the second event will change because of what happened first.
The probability of two dependent events, A and B, is equal to the probability of event A times the probability of event B. However, the probability of event B now depends on event A.
P(A, B) = P(A) P(B)Slide 8
Dependent Event
6 3 or
14 7
5
13
3 5 15 or
7 13 91
Example: There are 6 black pens and 8 blue pens in a jar. If you take a pen without looking and then take another pen without replacing the first, what is the probability that you will get 2 black pens?
P(black second) = (There are 13 pens left and 5 are black)
P(black first) =
P(black, black) =
THEREFORE………………………………………………
Slide 9
TEST YOURSELFAre these dependent or independent events?
1. Tossing two dice and getting a 6 on both of them.
2. You have a bag of marbles: 3 blue, 5 white, and 12 red. You choose one marble out of the bag, look at it then put it back. Then you choose another marble.
3. You have a basket of socks. You need to find the probability of pulling out a black sock and its matching black sock without putting the first sock back.
4. You pick the letter Q from a bag containing all the letters of the alphabet. You do not put the Q back in the bag before you pick another tile.
Slide 10
Find the probability
• P(jack, factor of 12) 1
5
5
8x =
5
40
1
8
Independent Events
Slide 11
Find the probability
• P(6, not 5)1
6
5
6x =
5
36
Independent Events
Slide 12
Find the probability• P(Q, Q)• All the letters of the
alphabet are in the bag 1 time
• Do not replace the letter
1
26
0
25x =
0
650
0
Dependent Events
Slide 13
Top Related