Tree Diagram Notes
Example:
A bag contains 3 black balls and 5 white balls. Paul picks a ball at random from the bag and replaces it
back in the bag. He mixes the balls in the bag and then picks another ball at random from the bag.
Construct a probability tree of the problem.
Calculate the probability that Paul picks:
i) two black balls
ii) a black ball in his second draw
Example:
Bag A contains 10 marbles of which 2 are red and 8 are black. Bag B contains 12 marbles of which 4 are
red and 8 are black. A ball is drawn at random from each bag.
Draw a probability tree diagram to show all the outcomes the experiment.
Find the probability that:
(i) both are red.
(ii) both are black.
(iii) one black and one red.
(iv) at least one red.
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Example: A box contains 4 red and 2 blue chips. A chip is drawn at random and then replaced. A second
chip is then drawn at random.
Show all the possible outcomes using a probability tree diagram.
Calculate the probability of getting:
(i) at least one blue.
(ii) one red and one blue.
(iii) two of the same color
Example: Jerry has a bag with seven blue sweets and 3 red sweets in it. She picks up a sweet at random
from the bag, replaces it and then picks again at random. Draw a tree diagram to represent this situation.
Use the diagram to calculate the probabilities that she picks:
(a) two red sweets
(b) no red sweets
(c) at least one blue sweet
(d) one sweet of each color
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Practice"
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1.! Tom"can"order"a"thick"or"thin!crust"pizza"with"2"different"toppings."The"choices"of"toppings"are"
mushroom"and"onions."Draw"a"tree"diagram"that"shows"every"possible"combination"of"a"pizza"that"
Tom"can"order."
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2.! A"bottle"has"1"green"ball"and"2"red"balls."A"ball"is"drawn"at"random"and"replaced"in"the"bottle,"and"
another"ball"is"drawn."Create"a"tree"diagram"and"find"the"probability"of"drawing"green"ball"both"
times."
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3.! The"two"spinners"are"spun"together."Create"a"tree"diagram"to"find"the"probability"for"which"the"sum"
of"numbers"on"the"two"spinners"is"8.!
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4."Ed"has"a"box,"which"has"2"milk"chocolates"(D),"2"dark"chocolates"(P)"and"2"Milky"bars"(M)."Create"a"tree"diagram"
to"model"all"possible"outcomes."
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What"is"the"probability"of"picking"two"chocolates"of"the"same"flavor"without"looking?
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Four queen cards are placed on the table. A coin is tossed and one of the queen is chosen simultaneously.
Create a tree diagram to represent the possible outcomes.
What is the probability of getting a tail on the coin and the queen of diamonds?
Tony went to a restaurant. Two desserts and four beverages were available there. The desserts were Ice
cream and Pudding. The beverages were Orange juice, Coffee, Tea and Milk shake. Use a tree diagram
and find the different combinations of beverages and desserts from which Tony had to select.
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Simon must wear either a yellow shirt (YS) or a green shirt (GS) with a white trouser (WT) or a black
(BT) trouser. Use a tree diagram and find the number of combinations of shirts and trousers he can wear.
Matt wants to buy a car. He has to choose between 2 brands of cars, Camry and BMW. The two brands
come with a gray or black interior. Draw a tree diagram to represent all possibilities.
Find the probability of choosing a Camry with Gray interior.
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Complete!the!tree!diagram!by!writing!in!the!probabilities!for!each!branch!and!then!calculating!the!probabilities!
for!each!possible!outcome.!
a)"Bag"#1"has"2"white"and"3"red"marbles"and"bag"#2"has"4"purple,"2"green"and"1"orange.""Pick"from"bag"#1"keep"it"
and"then"pick"from"bag"#2."
PURPLE
2
5 WHITE
2
GREEN
7
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P(WP)-=P(WG)-=- 2 X 2 =
5
7
4
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ORANGE P(WO)-=PURPLE P(RP)-=RED
GREEN
P(RG)-=-
ORANGE P(RO)-=-
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b)"A"bag"of"marbles"has"15"red"and"5"green.""Two"picks"are"made"from"the"same"bag"without"replacement.!
Red
Red
!
P(RR)*=*
Green P(RG)*=*
Red
P(GR)*=*
Green
Green P(GG)*=*
!
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