The contingency table below summarizes a survey of 1,000 bottled beverage consumers. Lives in a state with a deposit law Lives in a state with no deposit law Row Total Recycles beverage bottles 137 180 317 Does not recycle beverage bottles 60 623 683 Column Total 197 803 1,000 Find the following probabilities or percentages: (a) Probability that a consumer recycles beverage bottles. (Round your answer to 2 decimal places.) P(Recycles) (b) Probability that a consumer who lives in a state with a deposit law does not recycle. (Round your answer to 2 decimal places.) P(Don’t Recycle | Lives in Deposit Law State) (c) Percentage of consumers who recycle and live in a state with a deposit law. (Round your answer to 1 decimal place.) Percentage of consumers % (d) Percentage of consumers in states with a deposit law who recycle. (Round your answer to the nearest whole percent.) Percentage of consumers %
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
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| Lives in a state with a deposit law | Lives in a state with no deposit law | Row Total | |||||||||
| Recycles beverage bottles | 137 | 180 | 317 | ||||||||
| Does not recycle beverage bottles | 60 | 623 | 683 | ||||||||
| Column Total | 197 | 803 | 1,000 | ||||||||
Find the following probabilities or percentages:
(a)
P(Recycles)
(b) Probability that a consumer who lives in a state with a deposit law does not recycle. (Round your answer to 2 decimal places.)
P(Don’t Recycle | Lives in Deposit Law State)
(c) Percentage of consumers who recycle and live in a state with a deposit law. (Round your answer to 1 decimal place.)
Percentage of consumers %
(d) Percentage of consumers in states with a deposit law who recycle. (Round your answer to the nearest whole percent.)
Percentage of consumers %
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