Question

Two players play a tennis match. It is known that the probability of winning the match by the first player is 0.62. What is the probability of winning the match by the second player?

Answer 1

Hint: Here we use the concept that in a two player game either player 1 wins or player 2 wins. We are given the probability of the first player, so using the fact that the sum of probabilities of two players wins will be equal to 1, we can find the probability of the second player winning the game.
* Probability of an event is favorable outcomes divided by total number of observations.

Complete step-by-step answer:
We are given that in the tennis match two players are playing.
Consider \[{P_1}\] be the win of the first player and \[{P_2}\] be the win of the second player.
Let us denote the probability of the first player winning the tennis match be \[P({P_1})\] and the probability of the first player winning the tennis match be \[P({P_2})\].
Probability of first player winning the game is 0.62
\[ \Rightarrow P({P_1}) = 0.62\]
Since, we know \[P({P_1}) + P({P_2}) = 1\]
Therefore, \[0.62 + P({P_2}) = 1\]
Shift all constants to one side of the equation.
\[ \Rightarrow P({P_2}) = 1 - 0.62\]
\[ \Rightarrow P({P_2}) = 0.38\]

So, the probability of the second player winning the tennis match is 0.38.

Note: Students many times make mistake when they consider that probability of winning the game and losing the game are equal i.e. \[\dfrac{1}{2}\] and then they try to solve the question including the method of probability of win and loss, but this is not necessary in this solution because we are given the probability of win and we have to find probability of win.
Also, keep in mind that probability of an event is always less than or equal to 1 and greater than or equal to 0.