Probability using the complement rule

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In summary, the probability of none of the eight households using a cell phone exclusively is approximately 17.7%. The probability of at least one household using the cell phone exclusively is approximately 82.3%. And the probability of at least five households using the cell phone exclusively is approximately 0.4%.
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"It is reported that 16 percent of American households use a cell phone exclusively for their tele- phone service. In a sample of eight households, find the probability that:
a. None use a cell phone as their exclusive service.
b. At least one uses the cell exclusively.
c. At least five use the cell phone.
 
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  • #2
trastic said:
"It is reported that 16 percent of American households use a cell phone exclusively for their tele- phone service. In a sample of eight households, find the probability that:
a. None use a cell phone as their exclusive service.
b. At least one uses the cell exclusively.
c. At least five use the cell phone.

This is a binomial distribution with n = 8 and p = 0.16.
 

FAQ: Probability using the complement rule

What is the complement rule in probability?

The complement rule in probability states that the probability of an event not occurring is equal to 1 minus the probability of the event occurring. This can be represented mathematically as P(A') = 1 - P(A), where A is the event and A' is the complement of the event.

How is the complement rule used in probability calculations?

The complement rule is used in probability calculations to find the probability of an event not occurring. This is particularly useful when the probability of an event occurring is difficult to calculate directly. By finding the complement, we can subtract it from 1 to find the desired probability.

Can the complement rule be applied to any type of probability problem?

Yes, the complement rule can be applied to any type of probability problem. It is a fundamental concept in probability theory and can be used in a wide range of scenarios, including discrete and continuous probability distributions, as well as in conditional probability problems.

How does the complement rule relate to the addition rule of probability?

The complement rule and the addition rule of probability are closely related. The addition rule states that the probability of the union of two events is equal to the sum of their individual probabilities minus the probability of their intersection. This can also be expressed as P(A or B) = P(A) + P(B) - P(A and B). The complement rule is simply a special case of the addition rule where one of the events is the complement of the other.

Are there any limitations to using the complement rule in probability?

The complement rule is a useful tool in probability calculations, but it does have some limitations. It assumes that the events are independent, meaning that the occurrence of one event does not affect the occurrence of the other. If this assumption is not met, the complement rule may not be applicable. Additionally, the complement rule can only be used for events with two possible outcomes (i.e. success or failure).

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