Question

Question 3 [15 Marks]

3.1 Answer questions a, b and c below:

a) If we roll a fair die and toss a coin, the total number of possible outcomes is: [2]

b) If we roll a fair 4-sided die 3 times, the total number of possible outcomes is: [2]

c) Teams M and N play in a basketball tournament. The team that first wins three games wins the

tournament. Draw the tree diagram that present all possible course of the tournament. [6]

c

3.2 Find 𝑥 if 2𝑃(𝑥,2) + 50 = 𝑃(2𝑥,2)

Answer 1

a) When you flip a coin there are two possible outcomes (heads or tails) and when you roll a die there are six outcomes(1 to 6). Putting these together means you have a total of $2(6)=12$ outcomes.

b) If we multiply the total number of sides of each dice together we get the total number of possible combinations. So to calculate the number for three 4-sided dice we need to do

$$4 × 4 × 4 =4^3= 64$$

combinations.

c)

d)

$$P(x, 2)=\dfrac{x!}{(x-2)!}=x(x-1)$$

$$P(2x, 2)=\dfrac{(2x)!}{(2x-2)!}=2x(2x-1)$$

Substitute

$$2x(x-1)+50=2x(2x-1)$$

$$2x^2-2x+50=4x^2-2x$$

$$2x^2=50$$

$$x^2=25$$

Since $x\geq2,$ we take $x=5.$

$x=5$