The probabilities that a service station will pump gas into...

The probabilities that a service station will pump gas into $0,1,2,3,4,$ or 5 or more cars during a certain 30-minute period are 0.03,0.18,0.24,0.28 , $0.10,$ and $0.17,$ respectively. Find the probability that in this 30 -minute period (a) more than 2 cars receive gas; (b) at most 4 cars receive gas; (c) 4 or more cars receive gas.

The probabilities that a service station will pump gas into $0,1,2,3,4,$ or 5 or more cars during a certain 30-minute period are 0.03,0.18,0.24,0.28 , $0.10,$ and $0.17,$ respectively. Find the probability that in this 30 -minute period
(a) more than 2 cars receive gas;
(b) at most 4 cars receive gas;
(c) 4 or more cars receive gas.

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Key Concepts

Discrete Probability Distribution

A discrete probability distribution specifies the probability of each distinct outcome in a finite or countable set. In problems like this, the distribution assigns a probability to each possible number of cars being served, allowing precise calculations of the likelihood for each event.

Cumulative Probability

Cumulative probability involves summing the probabilities for a range of outcomes up to a certain value (or beyond a certain threshold). This concept enables one to compute the probability of a compound event, such as 'at most' or 'more than' a certain number of occurrences, by accumulating the individual probabilities associated with each outcome.

Complement Rule

The complement rule states that the probability of an event not occurring is equal to one minus the probability that it does occur. This principle is useful in situations where calculating the probability of the complement event (e.g., 'not more than 2 cars') is easier than directly calculating the event itself.

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