Two teams are playing a game. The format is best of 7 (first team to win four games wins). Each game can only be won or lost, not tied. Is a team more likely to win in 6 games, or 7?
Answers
Given : Two teams are playing a game. The format is best of 7 (first team to win four games wins). Each game can only be won or lost, not tied.
To find : Is a team more likely to win in 6 games, or 7
Solution:
Team can win 6 games
if team win either 6 matches , 5 matches or 4 matches
Number of ways
⁶C₆ + ⁶C₅ + ⁶C₄
= 1 + 6 + 15
= 22
Team can win in 7 games
if team win either 7 matches , 6 matches , 5 matches or 4 matches
Number of ways
⁷C₇ + ⁷C₆ + ⁷C₅ + ⁷C₄
= 1 + 7 + 21 + 35
= 64
But if Question is 6th game or 7th game
To win in 6th game
Then till 5th game team has win 3 match out of 5 & 6th has to win
= ⁵C₃ * 1
= 10 Ways
To win in 7th game
Then till 6th game team has win 3 match out of 6 & 7th has to win
= ⁶C₃ * 1
= 20 Ways
in both cases its more likely to win in 7 games
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Answer:
What two teams are playing answer