4. 3. John has 5 shirts; 2 red, 1 black and 2 blue. he has 3 hates; 1 red 1 white and 1
orange. he also has 4 pairs of pants; 2 blue 1 black and 1 tan.
a) Draw a tree diagram to represent the total number
of outfits john can wear.
b) what is the probability that John will wear a color
other than blue?
c) if john doesn't want to wear the same colour twice in
one outfit, how many total different outfits are possible?
4
5. a) Draw a tree diagram to represent the total number of
B
B
outfits john can wear.
Bl
TB
R B
P(wearing one of the shirts)
Bl
W BT
R 1
_
B
because, he can only wear 1
Bl =
O
5 shirt out of 5 possible ones.
TB
B
R Bl Where;
T
B
B
W
R = red
Bl B
P(wearing one of the hats)
R TB Bl = black
O
Bl B = blue
BT 1 wear one hat possible
_ W = white
R B = choices. O = orange
Bl B
3
TB T = tan
Bl W
Bl
BT
O B
Bl
P(wearing one pair of pants)
BT
R
B
B
B Bl
1
W B
_
T wear one pair of pants possible
=
Bl
B
choices.
4
T
B
O
Bl
B T
R B
Bl B
B W T B
Bl
B
O T
B
Bl
T
5
6. R
R
To start, we branch out the
Step 1.
number of shirts he has
Bl
B
B
6
7. R
W
R
O
R
W
R O
Step 2.
R
Bl W
O
We then branch out the possible hats
John could wear with his shirts
R
B W
O
R
B W
O
7
8. B
B
Bl
TB
R B
Bl
Step 3.
W BT
R B
Bl
O
TB
B
R Bl
T
B
Then we branch off the possible pants he
B
W
Bl B
could wear.
R TB
O
Bl
BT
R B
Bl B
TB
Bl W
Bl
Step 4.
BT
O B
Bl
BT
R
B
B
B Bl
W B
Last but not least, we label the
T
Bl
B
T
B
O
probability of each piece of clothing.
Bl
B T
R B
Bl B
B W T B
Bl
B
O T
B
Bl
T
8
9. P(wearing one of the shirts)
1
_ because, he can only wear 1
=
5 shirt out of 5 possible ones.
P(wearing one of the hats)
1 wear one hat possible
_
= choices.
3
P(wearing one pair of pants)
1
_ wear one pair of pants possible
=
choices.
4
9
11. b) what is the probability that John will wear a color
other than blue?
_ and simplified to;
3 2
3
_ _ _ 18
=
5 4
3 60
_
3
10
also can be
simplified into
percentage;
30% Of the outfits that don't
have blue.
11
12. b) what is the probability that John will wear a color
other than blue?
Step 1. To solve this problem, we start by looking at the diagram and exclude the
outfit with blue in them.
.
_
3 of the shirts are not blue
5
3
_ . of the hats are not blue
3
2 .
_ of the pants are not blue
4
12
13. Step 2. Because John will wear a shirt and a hat and a pair
of pants, we muliply the fractions we found of
clothing that are not blue.
._ =_
.4 3
2
3
_ _ 18
5 3 60
13
14. c) If john doesn't want to wear the same
colour twice in one outfit, how many
total different outfits are possible?
14
15. c) if john doesn't want to wear the same colour twice in
one outfit, how many total different outfits are possible?
RRB
Bl R B B R B
RRB
6
B R B
Bl R B
6
RRBl
B R Bl
Bl R Bl
outfits
RRT
B R T
outfits Bl R T
RWB
Bl W B B W B
with
with
RWB Bl W B B W B
Bl W Bl B W Bl
RWBl
blue
red Bl W T B W T
RWT
Bl O B B O B
shirts
ROB
shirts. Bl O B B O B
B O Bl
ROB Bl O Bl
B O T
Bl O T
ROBl
ROT
15
16. c) if john doesn't want to wear the same colour twice in
one outfit, how many total different outfits are possible?
RRB We take the same approch to solve this problem in that we look at the tree
diagram. this time we write out the total possible outfits, which in this case,
RRB it's called the quot;sample spacequot;.
RRBl
RRT
RWB
we eleminate the outfits with the same
Step 1.
color twice and duplicate combinations.
RWB
RWBl
RWT
X 2 because 2 red shirts.
ROB
ROB
ROBl
6 outfits with red shirts.
ROT
16
17. c) if john doesn't want to wear the same colour twice in
one outfit, how many total different outfits are possible?
We total up the remaining combinations
Step 2.
Bl R B B R B
B R B
Bl R B
B R Bl
Bl R Bl
X 2 because 2 blue shirts
B R T
Bl R T
Bl W B B W B
Bl W B B W B
6 outfits with blue shirts
Bl W Bl B W Bl
Bl W T B W T
Bl O B B O B
Bl O B B O B
B O Bl
Bl O Bl
7 outfits with black shirt B O T
Bl O T
17
