Given four integers p, q, r and s. Two players are playing a game where both the players are hitting a target and the first player who hits the target wins the game, the probability of the first player hitting the target is p / q and as that of second player hitting the target is r / s. The task is to find the probability of the first player winning the game.
Input: p = 1, q = 4, r = 3, s = 4
Input: p = 1, q = 2, r = 1, s = 2
Approach: The probability of the first player hitting the target is p / q and missing the target is 1 – p / q.
The probability of the second player hitting the target is r / s and missing the target is 1 – r / s.
Let, the first player be x and the second player be y.
So the total probability will be x won + (x lost * y lost * x won) + (x lost * y lost * x lost * y lost * x won) + … so on.
Because x can win in any turn, Its an infinite sequence.
Let t = (1 – p / q) * (1 – r / s). Here t < 1 as p / q and r / s are always <1.
So the series will become, p / q + (p / q) * t + (p / q) * t2 + …
This is an infinite GP series with common ratio less than 1 and it’s sum will be (p / q) / (1 – t).
Below is the implementation of the above approach:
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
- Probability of A winning the match when individual probabilities of hitting the target given
- Largest odd divisor Game to check which player wins
- Two player game in which a player can remove all occurrences of a number
- Find the player who will win the Coin game
- Find the minimum possible health of the winning player
- Write a function that generates one of 3 numbers according to given probabilities
- Find amount to be added to achieve target ratio in a given mixture
- Find minimum moves to reach target on an infinite line
- Puzzle | Find The Probability of Distance in a Square
- Find the probability of reaching all points after N moves from point N
- Find probability of selecting element from kth column after N iterations
- Game of N stones where each player can remove 1, 3 or 4
- Minimum moves to reach target on a infinite line | Set 2
- Probability of rain on N+1th day
- Aptitude | Probability | Question 2
- Aptitude | Probability | Question 1
- Probability that two persons will meet
- Aptitude | Probability | Question 3
- Aptitude | Probability | Question 4
- Aptitude | Probability | Question 5
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.