Probability 4Core: Tree Diagrams
1Ben has a bag of sweets. He chooses one sweet from the bag at random.
The table shows the probability of each flavour being chosen.
Flavour / Strawberry / Lemon / Orange / BlackberryProbability / 0.35 / 0.05 / 0.1
aWhat is the probability that a randomly chose sweet is Blackberry flavoured?
bIf there are 20 sweets in the bag how many would you expect to be Orange flavoured.
2 A fair six sided die is rolled twice. Copy and complete the tree diagram to show the possible outcomes.
a) What is the probability that you roll two sixes?
b) What is the probability that you roll at least one six?
3aDraw a tree diagram to show the possible outcomes when a fair coin is tossed three times.
bWhat is the probability of getting
i3 Heads
ii2 Heads and 1 Tail (in any order)?
4A box of chocolates contains 10 hard centres and 6 soft centres.
Three chocolates are chosen randomly and eaten one after the other..
aDraw a tree diagram to show all possible outcomes.
bCalculate the probability that:
i three hard centres are chosen
ii at least one hard centre is chosen
iii at least two soft centres are chosen.
4aExplain how multiplying a fraction by a whole number can help you to work out the expected number of successes when an experiment is repeated. Give an example.
bThe probability of winning a game is . How many wins would you expect if you played the game 100 times?
1Eddie and Steve play a game of darts.
They each throw one dart.
The probability that Eddie hits bullseye is .
The probability that Steve hits bullseye is .
Find the probability that:
aboth hit the bullseye
bonly one hits the bullseye
2A box of coloured files is passed around class 9T.
There are 9 purple, 4 yellow and 15 blue files in the box.
Rosanna and Sarah, in that order, are given a file at random.
aDraw a tree diagram to show all the probabilities of the coloured files that Rosanna and Sarah could get.
bCalculate the probability that Sarah gets a purple file.
cCalculate the probability that both girls get the same colour file.
4In a tombola, tickets numbered 1–50 are put in a drum.
If you pick a ticket that ends in a 0 or a 5, you win a prize.
aRajesh picks a ticket. What is the probability that he wins a prize?
Sebastian picks a ticket after Rajesh.
What is the probability that:
bthey both win a prize
cneither of them wins a prize?
4Sammy decided to test the truth of the statement:
‘Buttered bread, when dropped, always lands butter side down.’
He dropped a piece of buttered bread in sets of 10 drops. He recorded his results in the table below.
Set of 10 drops / 1 / 2 / 3 / 4 / 5 / 6Number butter side down / 9 / 8 / 8 / 7 / 9 / 8
Relative frequency
aCopy the table and calculate the relative frequency of bread landing butter side down.
bDo you think that the statement is true?Give a reason for your answer.