The problem consists of three parts. (b)(i): Two fair-sided coins are tossed. List all the four possible outcomes using H for Heads and T for Tails. (b)(ii): Find the probability of getting two Heads or two Tails. (c): Solve the equation $2^{2x-1} = 64$.

1. Problem Description

The problem consists of three parts.

(b)(i): Two fair-sided coins are tossed. List all the four possible outcomes using H for Heads and T for Tails.

(b)(ii): Find the probability of getting two Heads or two Tails.

(c): Solve the equation $2^{2x-1} = 64$.

2. Solution Steps

(b)(i): The possible outcomes of tossing two coins are: HH, HT, TH, TT.

(b)(ii): There are four possible outcomes: HH, HT, TH, TT.

The event of getting two Heads is HH. The event of getting two Tails is TT.

The number of favorable outcomes for two Heads or two Tails is

2. The total number of possible outcomes is

4. The probability of getting two Heads or two Tails is $\frac{2}{4} = \frac{1}{2}$.

(c): We have the equation $2^{2x-1} = 64$.

Since $64 = 2^6$, we can rewrite the equation as:

$2^{2x-1} = 2^6$.

Therefore, the exponents must be equal:

$2x - 1 = 6$.

Add 1 to both sides:

$2x = 7$.

Divide both sides by 2:

$x = \frac{7}{2} = 3.5$.

3. Final Answer

(b)(i): HH, HT, TH, TT

(b)(ii): $\frac{1}{2}$

(c): $x = \frac{7}{2}$