At the end of regulation time, a basketball team is trailing by one point and a player goes to the line for two free throws. If the player makes exactly one free throw, the game goes into overtime. The probability that the first free throw is good is 3/5. If the first attempt is good, the player relaxes and the second attempt is good with probability 4/5. However, if the player misses the first attempt, the added pressure reduces the success probability of the second attempt to 1/3. (a) What is the probability that the basketball team wins at the end of regulation time? (b) What is the probability that the game goes into overtime?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
At the end of regulation time, a basketball team is trailing by one point and a player goes to the line for two free throws. If the player makes exactly one free throw, the game goes into overtime. The probability that the first free throw is good is 3/5. If the first attempt is good, the player relaxes and the second attempt is good with probability 4/5. However, if the player misses the first attempt, the added pressure reduces the success probability of the second attempt to 1/3.
(a) What is the probability that the basketball team wins at the end of regulation time?
(b) What is the probability that the game goes into overtime?
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