An experiment consists of rolling a weighted die. The probability of rolling each number is: Pr[1]=0.2, Pr[2]=0.1, Pr[3]=0.3, Pr[4]=0.2, Pr[5]=0.1, and Pr[6]=0.1. On the first roll, you record if the number is Small (1,2,3) or Large (4,5,6). If the first number is Small, then on the second roll you record if the number is a 5 or not. If the first number is Large, on the second roll you record whether the number is Small or not. So, some typical outcomes would be S5 (small number rolled, then 5) or LL (large number rolled, then another large number). Draw a tree diagram and use it to answer the following questions. (1) What is Pr[S5]? (2) What is Pr[LS]? (3) What is Pr[(not5)onsecondroll|Sonfirstroll]? (4) What is Pr[Lonsecondroll|Lonfirstroll]?
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.
An experiment consists of rolling a weighted die. The probability of rolling each number is: Pr[1]=0.2, Pr[2]=0.1, Pr[3]=0.3, Pr[4]=0.2, Pr[5]=0.1, and Pr[6]=0.1. On the first roll, you record if the number is Small (1,2,3) or Large (4,5,6). If the first number is Small, then on the second roll you record if the number is a 5 or not. If the first number is Large, on the second roll you record whether the number is Small or not. So, some typical outcomes would be S5 (small number rolled, then 5) or LL (large number rolled, then another large number). Draw a tree diagram and use it to answer the following questions.
(1) What is Pr[S5]?
(2) What is Pr[LS]?
(3) What is Pr[(not5)onsecondroll|Sonfirstroll]?
(4) What is Pr[Lonsecondroll|Lonfirstroll]?
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