Half Time Scores
The final score of a football match is 6 to 3. How many different results are possible in the first half? 3
The final score of a football match is 6 to 3. w There are many possible outcomes in the first half.
In the range, the result can be 63, 62, 61, 60.
Or 53, 52, 5 1, 50
Or 43, 42, 41, 40
Or 33, 32, 3 1, 30
Or 23, 22, 2 1, 20
Or 13, 12, 11, 10
A03, 02, 0 1, 00
Total n is 7 * 4 = 28 possible different ratings
This problem can be very serious. Are the two teams different (ie the order in which the score of both teams is important)? I will examine both interpretations. a) Suppose the teams are differentiated in such a way that, for example, the result from 1 to 2 is assessed as a result different from the result from 2 to 1. In the first half, the result of the first team can n '. Any number from 0 to 6 and therefore it has 7 scoring chances. The other team's score can range from 0 to 3 and therefore has 4 possible values. According to the basic scoring principle, there are 7x4 = 28 possible scores in the game in the first half, if the scoring order of both teams is important. B) Assuming that the teams are not separated this time, so that, for example, the result of 1 to 2 is equal to the result of 2 to 1 team. With different scores, ie 0, 1, 2 or 3. Depending on the interpretation a) The sum of this type of interval score is 4x3 = 12. According to this interpretation b) There are only 12/2 = 6 half results. This kind of time for all other half-life results (ie, those that can only be in one order), both interpretations give the same value. In this case, the number of possible interval values according to this interpretation b) will be 126 = 6 less than the number of possible interval values according to interpretation a). There are 286 possible scores at half time if the ranking of both teams is not * important *. God bless you today!
At halftime, the starting lineup could score between 0 and 6, so there were 7 chances in total.
The other team could have scored between 0 and 3, 4 times in total.
They have 7 * 4 = 28 possible classifications.
