Cambridge Essentials MathematicsExtension 9S3.1 Homework2
/ S3.1 Homework 21A fair five-sided spinner is spun and a coin is tossed to land as a head or a tail.
aDraw a sample space diagram to show all the possible outcomes.
bFindthe probability the spinner will land as 3 or more and the coin will be ahead.
cWhat is the probability that the spinner will land on 3 or more?
dWhat is the probability that the coin will be a head?
eFind the probability that the spinner lands on 3 or more and the coin will be a head.
This time though, use your answer to parts c and d.
Is this the same as your answer to part b?
2Two six-sided dice are tossed.
aDraw a sample space diagram to show all the possible outcomes.
Use your diagram to find the probabilities.
bBoth dice land on the same number.
cThe sum of the two numbers is 9 or more.
dBoth numbers are prime.
eThe difference between the two numbers is 3.
3The probability that Mario walks to school is 0.7.
The probability that Kim walks to school is 0.4. These are independent events.
aWork out the probability that both Mario and Kim walk to school.
bFind the probability that Mario walks to school, but Kim does not walk to school.
cWork out the probability that neither Mario nor Kim walk to school
4A letter is posted with a first class stamp on it.
The probability it will be delivered on the next working day is 0.9.
Dee posts two letters with first class stamps.
This information has been used to draw a tree diagram.
Use the tree diagram to work out the probability.
aBoth letters are delivered the next working day.
bBoth letters are not delivered the next working day.
cOnly one letter is delivered the next working day.
5In fish tank x there are four cat fish and one tetra.
In fish tank y there are three cat fish and four tetras.
One fish is taken out of each tank at random.
aComplete the probability tree diagram.
bUse your tree diagram to work out these probabilities.
iBoth fish are cat fish.
iiNeither fish is a cat fish.
iiiOnly one fish is a cat fish.
6The probability that a new road needs repairing after one year is 0.18.
If it is not repaired the first year, the probability it needs repairing the next year is 0.62. If it is repaired in one year, the probability it needs repairing the next year is 0.02.
aDraw a tree diagram to show the repairs over the two years.
bCalculate these probabilities.
iThe road does not need repairing during the two years.
iiThe road only needs repairing in the second year.
7The probability that Annabel goes swimming is.
The probability that Annabel visits the library is . Both events are independent.
Work out these probabilities.
aAnnabel goes swimming and visits the library.
bAnnabel goes swimming but does not visit the library.
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