Year 9 Extra Homework
Chapter 9 Probability and statistics
1. The spinners below have equally divided sections. For each, list the sample space, and
find Pr(2), Pr(not 2), Pr(2 or 3), and Pr(at least 2).
a) b) c)
2. A letter is chosen at random form the word ALPHABET. Find the following probabilities.
a) Pr(L) b) Pr(A) c) Pr(A or L) d) Pr(not A)
e) Pr(vowel) f) Pr(consonant) g) Pr(vowel and consonant)
h) Pr(letter from the first half of the alphabet)
3. In a class of 30 students, 22 carried a phone and 9 carried an iPad. Three carried both a
phone and an iPad, and two carried neither.
a) Represent the information using a Venn diagram.
b) How many students:
i) carry a phone or an iPad or both ii) carry an iPad iii) carry only an iPad
c) If one student was selected at random, find:
i) Pr(carry a phone and an iPad) ii) Pr(carry neither) iii) Pr(carry only a phone)
4. From 50 desserts served at a restaurant, 25 were served with ice cream, 21 with cream
and 5 with both cream and ice cream.
a) Illustrate the situation using a two-way table.
b) How many desserts:
i) did not have cream ii) had neither cream nor ice cream
c) Find the probability that a chosen dessert:
i) had cream ii) had only cream iii) had cream or ice cream
5. A number is chosen from the set of integers between 1 and 10 inclusive. If A is the set of
odd numbers between them and B is the set of prime numbers between them:
a) List the sets: i) the sample space ii) A iii) B
iv) A B v) A B vi) A' vii) B only
b) Find: i) n(A) ii) Pr(A) iii) n(A B) iv) Pr(A B)
6. Two four-sided dice (numbered 1, 2, 3, 4) are tossed.
a) Complete the table.
b) Find the probability of obtaining (2,3).
c)
7. Two letters are chosen from the word DOG without replacement.
a) Complete the table.
b) Find the probability of obtaining (G,D).
c) Find the probability of obtaining an O in it.
8. A coin is tossed twice.
a) Complete the tree diagram.
b) Find the probability of obtaining:
i) two heads ii) one head iii) at least one head iv) at least one tail
9. Two people are selected without replacement from Donna (D), Elle (E) and Fernando (F).
a) List all the possible outcomes using a tree diagram.
b) Find the probability that the selection contains:
i) Donna and Elle ii) Fernando iii) Fernando or Elle
Enrich Maths 17
Chapter 9 Probability and statistics
1. The spinners below have equally divided sections. For each, list the sample space, and
find Pr(2), Pr(not 2), Pr(2 or 3), and Pr(at least 2).
a) b) c)
2. A letter is chosen at random form the word ALPHABET. Find the following probabilities.
a) Pr(L) b) Pr(A) c) Pr(A or L) d) Pr(not A)
e) Pr(vowel) f) Pr(consonant) g) Pr(vowel and consonant)
h) Pr(letter from the first half of the alphabet)
3. In a class of 30 students, 22 carried a phone and 9 carried an iPad. Three carried both a
phone and an iPad, and two carried neither.
a) Represent the information using a Venn diagram.
b) How many students:
i) carry a phone or an iPad or both ii) carry an iPad iii) carry only an iPad
c) If one student was selected at random, find:
i) Pr(carry a phone and an iPad) ii) Pr(carry neither) iii) Pr(carry only a phone)
4. From 50 desserts served at a restaurant, 25 were served with ice cream, 21 with cream
and 5 with both cream and ice cream.
a) Illustrate the situation using a two-way table.
b) How many desserts:
i) did not have cream ii) had neither cream nor ice cream
c) Find the probability that a chosen dessert:
i) had cream ii) had only cream iii) had cream or ice cream
5. A number is chosen from the set of integers between 1 and 10 inclusive. If A is the set of
odd numbers between them and B is the set of prime numbers between them:
a) List the sets: i) the sample space ii) A iii) B
iv) A B v) A B vi) A' vii) B only
b) Find: i) n(A) ii) Pr(A) iii) n(A B) iv) Pr(A B)
6. Two four-sided dice (numbered 1, 2, 3, 4) are tossed.
a) Complete the table.
b) Find the probability of obtaining (2,3).
c)
7. Two letters are chosen from the word DOG without replacement.
a) Complete the table.
b) Find the probability of obtaining (G,D).
c) Find the probability of obtaining an O in it.
8. A coin is tossed twice.
a) Complete the tree diagram.
b) Find the probability of obtaining:
i) two heads ii) one head iii) at least one head iv) at least one tail
9. Two people are selected without replacement from Donna (D), Elle (E) and Fernando (F).
a) List all the possible outcomes using a tree diagram.
b) Find the probability that the selection contains:
i) Donna and Elle ii) Fernando iii) Fernando or Elle
Enrich Maths 17
