Player of the Season!

Discrete Mathematics Level 5

As EPL is about to end this season, Manchester United decides to choose the player of the season. For this they nominated De Gea, Rooney and Mata for this prestigious award. All the three players played exceptionally well this season. So the officials decide to write the shirt numbers of these players and put it in a box. A number is randomly picked up and put back. This was done four times. Now, they decided if the sum of the numbers is odd, then De Gea wins the award. If the sum is even, then Rooney and Mata will be selected for further methods of selection. What is the probability that De Gea wins the title?

The answer is of the form \(\dfrac{A}{B}\) for coprime positive integers \(A\) and \(B\). Find \(A+B\).

Details and Assumptions:

  • Shirt number of De Gea is 1.

  • Shirt number of Mata is 8.

  • Shirt number of Rooney is 10.


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