A sports team is playing in a tournament along with seven other teams. If they w

Question

A sports team is playing in a tournament along with seven other teams. If they win their first game, they proceed to the semifinals. If they win the semifinal game, they proceed to the final. If they win the final, they win the tournament. The coach calculates that they have a 0.6 chance of winning the round-of-eight game, a 0.5 chance of winning a semifinal game if they win their first game, and a 0.4 chance of winning the final if they win their first two games. What is the chance that they win the tournament? Given that they do not win the tournament, what is the chance that they played and lost the semifinal game?

Explanation / Answer

a)

the porbability that they win the tournament is winning the first game, the semifinal and the final so

P = 0.6 * 0.5 * 0.4 = 0.12

b)

P( lost semifinal / lost the tournament ) = P( lost tournament / lost semifinal) * P( lost semifinal) / P( lost tournament)

P( lost tournament / lost semifinal ) = 0.6 * ( 1 -0.5 ) = 0.3

P( lost semifinal) = 0.5

P( lost tourament) = 1 - 0.12 = 0.88

P( lost seminfian / lost tournament) = 0.3 * 0.5   / 0.88 = 0.1705

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.