**20.1- Introduction**

Question 1 : A coin is flipped 4 times, Calculate the probability of getting 4 Heads?

**20.2- Sets**

Use language, notation and Venn diagrams to describe sets and

represent relationships between sets

Definition of sets:

e.g.

A = {x∶ x is a natural number}

B = {(x,y): y = mx + c}

C = {x∶ a ≤ x ≤ b}

D = {a,b,c…}

Includes using Venn diagrams to solve problems.

Notation:

Number of elements in set A n(A)

“… is an element of …” ∈

“… is not an element of …” ∉

Complement of set A A’

The empty set ∅

Universal set ξ

A is a subset of B A ⊆ B

A is a proper subset of B A ⊂ B

A is not a subset of B A ⊈ B

A is not a proper subset of B A ⊄ B

Union of A and B A ∪ B

Intersection of A and B A ∩ B

**20.3-Probability Spaces**

Question 1 : Here are some information about 150 students.

ξ = 150 students

C = students who study Chemistry (47+x)

P = students who study Physics (35 +x)

X = students who study both physics and Chemistry

The probability that a Physics student, chosen at random, also studies Chemistry is \(\frac{5}{12}\) . One of the 150 students is chosen at random.

Calculate the probability that the student does not study either Chemistry or Physics ?

**20.4-Tree diagrams**

Question 1 : Two ordinary fair dice are rolled. Complete the tree diagram?

**20.5- Conditional Probability**

Question 1 : A coin is thrown followed by a dice. What’s the probability of getting a Head followed by a 3? If you get a 3, What’s the probability that the coin was a Head?

**20.6- Summary and Review**

Question 1 : The probability that A is the outcome of an experiment is 0.2 . Calculate the probability that A is not the outcome?

**20.7 Assessment 20**

Question 1 : A coin is thrown 50 times. It lands on heads 31 times.

(a) Calculate the relative frequency it lands on heads?

Question 2 : A biased dice is thrown. Here are the probabilities of each.

**Score**

The dice is thrown 200 times.

Calculate the expected number of times the score will be odd?

**20.8- Lifeskills 3 : Getting ready**

Question 1 : There are only r red counters and g green counters in a bag. A counter is taken at random from the bag. The probability that the counter is green is\(\frac{3}{7}\) The counter is put back in the bag. 2 more red counters and 3 more green counters are put in the bag. A counter is taken at random from the bag. The probability that the counter is green is \(\frac{6}{13}\) Find the number of red counters and the number of green counters that were in the bag originally?