A tennis match is played as a series of POINTS, contained within GAMES, which in turn are contained within SETS.
Suppose Djokovic plays a set of tennis against Murray under these rules, and his probability of winning a point is 0.48. Assuming the probability of winning a point remains constant throughout, what would be the probability of Djokovic winning the set 7-5?
Let's first determine the probability of winning a single game:
To simplify notation, let $p = 0.48$.
Next, let $P(D)$ be the probability that Djokovic wins a single game.
$D$ can occur in the following disjoint situations:
Djokovic wins four points in a row: $p^4$.
Djokovic wins wins four points while Murray gets only one: $\dbinom{4}{1}p^4(1-p)$.
Djokovic wins four points while Murray gets only two: $\dbinom{5}{2}p^4(1-p)^2$.
Plus the probability that they reach Deuce and Djokovic eventually wins (probability to be determined).
Let $E$ be the event that they reach Deuce. This happens with probability: $\dbinom{6}{3}p^3(1-p)^3$
The probability that Djokovic will win from Deuce is:
$$P(D|E) = p^2+2p(1-p)P(D|E)$$
Solving for $P(D|E)$ gives $\dfrac{p^2}{1-2p+2p^2}$.
So, the probability of $P(D\cap E) = P(D|E)P(E) = \dbinom{6}{3}\dfrac{p^5(1-p)^3}{1-2p+2p^2}$
Thus:
$$P(D) = p^4\left( 1 + \dbinom{4}{1}(1-p) + \dbinom{5}{2}(1-p)^2 + \dbinom{6}{3}\dfrac{p(1-p)^3}{1-2p+2p^2} \right) = \dfrac{1375854336}{3056640625}$$
The only way for Djokovic to win 7-5 is if they tie at 5 games each, then Djokovic wins two in a row. If $q = \dfrac{1375854336}{3056640625}$, then the probability of this happening is:
$$\dbinom{10}{5}q^7(1-q)^5 \approx 0.047428310143589076989815246904379009553045283963625581247$$