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13.2 Counting the Elements of Sets
13.2 Counting the Elements of SetsStudent Study GuideStudent Study Guide
List the integers from 1 to 20 inclusive that are1. Odd OR greater than
10
List the integers from 1 to 20 inclusive that are1. Odd OR greater than
10
1, 3, 5, 7, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
1, 3, 5, 7, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
List the integers from 1 to 20 inclusive that are2. Multiples of 3 AND
even
List the integers from 1 to 20 inclusive that are2. Multiples of 3 AND
even-Multiples of 3 = 3, 6, 9, 12, 15, 18
-Even = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
-Multiples of 3 = 3, 6, 9, 12, 15, 18
-Even = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
6, 12, 18
6, 12, 18
Each of the integers from 1 to 100 inclusive is written on a card and one card is drawn at random. Find the probability
that the integer is3. 25 OR greater than 45
Each of the integers from 1 to 100 inclusive is written on a card and one card is drawn at random. Find the probability
that the integer is3. 25 OR greater than 45
*25 = 1 outcome*Greater than 45 = 100-45 = 55
55+1=56
*25 = 1 outcome*Greater than 45 = 100-45 = 55
55+1=56
56
100
56
100
= 14 25
= 14 25
Each of the integers from 1 to 100 inclusive is written on a card and one
card is drawn at random. Find the probability that the integer is
4. Even OR less than or equal to 30
Each of the integers from 1 to 100 inclusive is written on a card and one
card is drawn at random. Find the probability that the integer is
4. Even OR less than or equal to 30-Even = 2, 4, 6, … 100 = 50-Less than or equal to 30 = 30*50+30 = 80*2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30 - repeats
*80-15 = 65
-Even = 2, 4, 6, … 100 = 50-Less than or equal to 30 = 30*50+30 = 80*2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30 - repeats
*80-15 = 65
List the integers from 1 to 20 inclusive that are multiples of the following number: 6
List the integers from 1 to 20 inclusive that are multiples of the following number: 6
6, 12, 186, 12, 18
List the integers from 1 to 20 inclusive that are multiples of the following number: 9
List the integers from 1 to 20 inclusive that are multiples of the following number: 9
9, 189, 18
List the integers from 1 to 20 inclusive that are
multiples of the following numbers: 6 AND
9
List the integers from 1 to 20 inclusive that are
multiples of the following numbers: 6 AND
96= 6, 12, 18
9= 9, 186 and 9 = 18
6= 6, 12, 189= 9, 18
6 and 9 = 18
List the integers from 1 to 20 inclusive that are
multiples of the following numbers: 6 OR 9
List the integers from 1 to 20 inclusive that are
multiples of the following numbers: 6 OR 9
6= 6, 12, 189= 9, 18
6 OR 9 = 6, 12, 9, 18
6= 6, 12, 189= 9, 18
6 OR 9 = 6, 12, 9, 18
If you draw a card at random from a complete deck of 52 playing cards what is the probability that you will draw
the cards below?9. An odd numbered card AND a red
card
If you draw a card at random from a complete deck of 52 playing cards what is the probability that you will draw
the cards below?9. An odd numbered card AND a red
cardOdd= 3, 5, 7, 9
Red= diamonds and heartsOdd and Red =
3D, 5D, 7D, 9D, 3H, 5H, 7H, 9H
Odd= 3, 5, 7, 9Red= diamonds and hearts
Odd and Red = 3D, 5D, 7D, 9D, 3H, 5H, 7H,
9H8 52
2 13
If you draw a card at random from a complete deck of 52 playing cards what is the probability that
you will draw the cards below?9. An odd numbered card OR a red card
If you draw a card at random from a complete deck of 52 playing cards what is the probability that
you will draw the cards below?9. An odd numbered card OR a red card
Odd= 1, 3, 5, 7, 9 = 5 5 x 4 (suits) = 20
Red= diamonds (13), hearts (13) *26 red cards
20+26= 46*1D, 3D, 5D, 7D, 9D, 1H, 3H, 5H, 7H, 9H
- repeat = 10*46-10=36
Odd= 1, 3, 5, 7, 9 = 5 5 x 4 (suits) = 20
Red= diamonds (13), hearts (13) *26 red cards
20+26= 46*1D, 3D, 5D, 7D, 9D, 1H, 3H, 5H, 7H, 9H
- repeat = 10*46-10=36
36 52
= 9 13
14. How many of those surveyed are freshmen AND oppose requirement?
14. How many of those surveyed are freshmen AND oppose requirement?
4
Favor R Oppose R Total
Freshman 12 4 16
Sophomore
6 8 14
Junior 9 15 24
Senior 2 21 23
Total 29 48 77
15. How many of those surveyed are freshmen OR oppose requirement?
15. How many of those surveyed are freshmen OR oppose requirement?
Freshman = 16Oppose = 4816+48 = 64
Favor R Oppose R Total
Freshman 12 4 16
Sophomore
6 8 14
Junior 9 15 24
Senior 2 21 23
Total 29 48 77
4 repeat64-4=60
16. How many of those surveyed are juniors AND favor the requirement?16. How many of those surveyed are juniors AND favor the requirement?
9
Favor R Oppose R Total
Freshman 12 4 16
Sophomore
6 8 14
Junior 9 15 24
Senior 2 21 23
Total 29 48 77
17. How many of those surveyed are juniors OR favor the requirement?
17. How many of those surveyed are juniors OR favor the requirement?
Juniors = 24Favor = 2924+29=53
Favor R Oppose R Total
Freshman 12 4 16
Sophomore
6 8 14
Junior 9 15 24
Senior 2 21 23
Total 29 48 77
9 repeat53-9=44
