Recall that the fair price to play the game is equal to the expected payoff. We see that we will win £100 if we throw 2 or 3 heads. As a result, the expected payoff is $$ E[\text{Payoff}] = 100 \cdot \left( P(2H, 1T) + P(3H) \right). $$ To calculate the probabilities we use the binomial distribution. Recall that the binomial distribution is $$ f(p, n ,k) = {n \choose k} p^k (1-p)^{n-k}. $$ In our case, $$ P(k H\text{s}) = {3 \choose k} 0.45^k 0.55^{3-k}. $$ Evaluating this function for $k=2$ and $k=3$ gives $$ P(2H\text{s}) + P(3H\text{s}) = 0.4253. $$ Therefore, the fair price of this game is £42.53.