An insurance company estimated that 30% of all automobile accidents were partly caused by weather conditions and that 20% of all automobile accidents involved bodily injury. Further, of those accidents that involved bodily injury, 40% were partly caused by weather conditions. a. What is the probability that a randomly chosen accident both was partly caused by weather conditions and involved bodily injury? b. Are the events “partly caused by weather conditions” and “involved bodily injury” independent? c. If a randomly chosen accident was partly caused by weather conditions, what is the probability that it involved bodily injury? d. What is the probability that a randomly chosen accident both was not partly caused by weather conditions and did not involve bodily injury?
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 insurance company estimated that 30% of all automobile accidents were partly caused by weather conditions and that 20% of all automobile accidents involved bodily injury. Further, of those accidents that involved bodily injury, 40% were partly caused by weather conditions.
a. What is the probability that a randomly chosen accident both was partly caused by weather conditions and involved bodily injury?
b. Are the events “partly caused by weather conditions” and “involved bodily injury” independent?
c. If a randomly chosen accident was partly caused by weather conditions, what is the probability that it involved bodily injury?
d. What is the probability that a randomly chosen accident both was not partly caused by weather conditions and did not involve bodily injury?
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