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Tree Diagrams
•: “5sO’
Quick Review
Prepackaged lunches in the school cafeteria contain:
• a ham or a peanut-butter sandwich
• an apple or an orange
• juice or milk
How many different combinations of sandwich, fruit, and drink are there?
Draw a tree diagram.
Sandwich
Fruit
apple
ham
brink
jce
milk
juice
orane<,
juice
milk
peanut butter <aPPle
juice1
orange<
Combinations
h
pt’ juice
ham, apple, milk
ham, orange, juice
ham, orange, milk
peanut butter, apple, juice
peanut butter, apple, milk
peanut butter, orange, juice
peanut butter, orange, milk
There are 8 different combinations.
Try These
1.
Use the tree diagram above.
Suppose a student picks up a lunch package at random.
Find the probability of the student having each of the following:
a) a ham sandwich
b) anapple
C)
a peanut-butter sandwich and milk
d) a ham sandwich and an orange
e) a ham sandwich,juice, and an apple
f) a bologna sandwich
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Practice
1.
2.
Suppose you flip a penny, a nickel, and a dime.
Draw a tree diagram to show all the possible outcomes.
Use H for heads and T for tails.
Use the tree diagram from question 1 to determine the probab
ility of
flipping each of these combinations:
a) 2 heads and a tail
b) 2 tails and a head
C) 3 heads
d) 1
tail
3. The ice—cream shop offers 3 different flavours of ice cream
(vanilla, strawberry, cherry), 2 sauces (chocolate, marshmallow),
and
2 toppings (nuts, sprinkles). Draw a tree diagram to show all the possib
le
sundae orders with 1 flavour of ice cream, 1 sauce, and 1 toppin
g.
Stretch Your Thinking
In question 1 above, what is the difference between the outcom
e, HHT and the
outcome, HTH?
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