11. Two propositions are defined as follows: p: Louis plays the trumpet

q: Louis is part of the school band.

Write in symbolic form the following statements:

a) Louis plays trumpet and is in the school band.

b) If Louis plays the trumpet then he is in the school band.

c) Write a statement that describes the proposition,

q p

11. a) p q

b) p q

c) If Louis is not in the school band then he does not play the trumpet.

14. [Maximum mark: 7]

In a game a player rolls a biased four-faced die. The probability of each possible score is shown below.

Score 1 2 3 4

Probability 15

25

110

x

(a) Find the value of x. [2 marks]

(b) Find E ( )X . [3 marks]

(c) The die is rolled twice. Find the probability of obtaining two scores of 3. [2 marks]

13. A student chooses between Methods and Maths HL only. The probability of choosing Methods is 0.6. If the student chooses Methods the probability of he/she choosing Further Maths is 0.2. If the student chooses Maths HL the probability of choosing Further Maths is 0.5.

a) Complete the following tree diagram.

b) Calculate the probability of a student choosing to do Further Maths.

c) Given that the student chooses Further Maths, what is the probability that the student has chosen Methods?

13. a)

b) 0.32

c)

0.375 or

3

8

24. [Maximum mark: 10]

The probability of obtaining heads on a biased coin is 13

.

(a) Sammy tosses the coin three times. Find the probability of getting

(i) three heads;

(ii) two heads and one tail. [5 marks]

(b) Amir plays a game in which he tosses the coin 12 times.

(i) Find the expected number of heads.

(ii) Amir wins $ 10 for each head obtained, and loses $ 6 for each tail. Find his expected winnings. [5 marks]