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a. Car Trouble Problem: Mr. Rhees car has a 70% probability of starting, and Ms. Rhees
Chapter 9, Problem R.6(choose chapter or problem)
a. Car Trouble Problem: Mr. Rhees car has a 70% probability of starting, and Ms. Rhees car has a 80% probability of starting. Find the probability of each event.
i. Neither car will start.
ii. Both cars will start.
iii. Either both cars will start or neither car will start.
iv. Exactly one of the cars will start.
a. Basketball Game Problem: High school basketball teams often play each other twice during the season. Suppose Central High has a 60% probability of winning their first game against Tech. If Central wins the first game, they have an 85% probability of winning the second game. If Central loses the first game, they have a 45% probability of winning the second game. Find the probability of each of the following events.
i. Central wins both games.
ii. Central wins the first game and loses the second game.
iii. Central loses the first game and wins the second game.
iv. Central loses both games.
v. Show by calculation that the four answers above are reasonable.
Questions & Answers
QUESTION:
a. Car Trouble Problem: Mr. Rhees car has a 70% probability of starting, and Ms. Rhees car has a 80% probability of starting. Find the probability of each event.
i. Neither car will start.
ii. Both cars will start.
iii. Either both cars will start or neither car will start.
iv. Exactly one of the cars will start.
a. Basketball Game Problem: High school basketball teams often play each other twice during the season. Suppose Central High has a 60% probability of winning their first game against Tech. If Central wins the first game, they have an 85% probability of winning the second game. If Central loses the first game, they have a 45% probability of winning the second game. Find the probability of each of the following events.
i. Central wins both games.
ii. Central wins the first game and loses the second game.
iii. Central loses the first game and wins the second game.
iv. Central loses both games.
v. Show by calculation that the four answers above are reasonable.
ANSWER:Step 1 of 3
Let A be the event of Mr. Rhee’s car starting and B be the event of Ms. Rhee’s car starting.
Given:
Probability of Mr. Rhee’s car starting:
\(P(A) = 70\% = 0.7\)
Probability of Ms. Rhee’s car starting:
\(P(B) = 80\% = 0.8\)
Probability of Mr. Rhee’s car not starting:
\(P(A') = 1 - P(A) = 0.3\)
Probability of Ms. Rhee’s car not starting:
\(P(B') = 1 - P(B) = 0.2\)