Probability Revision
These problems you should be able to solve without difficulty.
1) A fair die is thrown once. Find the probability of obtaining a
a. a one
b. an odd number
c. number less than three
d. a prime number
2) One letter is selected from the word ‘MATHEMATICS’. Find the probability of selecting
a. an A
b. a M
c. a M or a T
d. a vowel
e. a K
3) A red die and a blue die are both thrown. Display all the possible outcomes on a probability space
diagram Find the probability of scoring
a. a total of 7,
b. more than 8,
c. less than 5.
4) A coin and a die are thrown. Write down the probability of obtaining
a. a head and an even number on the die
b. a tail and 3 or 4 on the die.
5) A study is made of a group of students. In the group there are 14 boys and 16 girls. Of the boys it is
found 8 of them like Mathematics and of the girls 10 like Mathematics. Draw a tree diagram and
find the probability that a student chosen at random
a. is a boy and likes Mathematics.
b. is a girl and does not like Mathematics
c. likes Mathematics.
Exam style problems
6)
7)
8)
Neal is attending a Scout jamboree in Japan. He has both boots and trainers to wear. He also
has the choice of wearing a cap or not.
The probability Neal wears boots is 0.4. If he wears boots, the probability that he wears a cap is
0.7.
If Neal wears trainers, the probability that he wears a cap is 0.25.
The following tree diagram shows the probabilities for Neal's clothing options at the jamboree.
(a) Find the value of A.
(b) Find the value of B.
(c) Find the value of C.
(d) Calculate the probability that Neal wears trainers and no cap.
(e) Calculate the probability that Neal wears no cap.
(f) Calculate the probability that Neal wears trainers given that he is not wearing a cap.
(g) Calculate the probability that Neal wears boots on the first two days of the jamboree.
(h) Calculate the probability that Neal wears boots on one of the first two days, and trainers on
the other.
9)
10)
Eels are elongated fish, ranging in length from 5cm to 4m. In a certain lake the length of the
eels are normally distributed with a mean of 84cm and a standard deviation of 18cm. Eels are
classified as giant eels if they are more than 120 cm long.
An eel is selected at random from the lake.
(a) Find the probability that this eel is a giant.
(b) Given that this eel is a giant, find the probability that it is longer than 130cm.
(c) Two eels are selected at random. Find the probability that they are both giants.
100 eels are selected at random.
(d) Find the expected number of these eels that are giants.
(e) Find the probability that at least 5 of these eels are giants.
A few challenging problems
11) There are two boxes, A and B. Box A contains 9 balls with 2 yellow, 3 red, and 4 black. Box B contains
9 balls with 3 yellow, 4 red, 2 black. If Adam selects one ball at random from box A and Betty selects
one from box B then what is the probability that they select the same color?
12) Adam has $6 and so does Betty. They take turns betting on the flip of a coin. If Adam lose he gives
Betty $1 and if Betty loses Adam gives her $1.
a. What is the probability that after 6 coin flips they both still have $6?
b. What is the probability that Adam has $1 left?
c. What is the probability that Adam has at least $2?