Understanding Geometric Random Variables

The video tutorial explains a probability problem involving Amelia, who registers vehicles for the Department of Transportation. The focus is on determining the probability that Amelia registers more than four vehicles before registering an SUV. The problem is modeled using a geometric random variable, as each vehicle registration is an independent trial with a constant probability of success. The tutorial walks through the calculation process, emphasizing the difference between geometric and binomial variables, and concludes with the final probability result.

What percentage of vehicles registered by Amelia are SUVs?

• 20%

• 10%

• 15%

• 12%

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What does the random variable V represent in this context?

• The number of non-SUVs registered in a day

• The number of SUVs registered in a day

• The number of vehicles registered until an SUV is registered

• The total number of vehicles registered in a day

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What type of random variable is V?

• Binomial random variable

• Poisson random variable

• Geometric random variable

• Normal random variable

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What is the probability of success in each trial?

• 0.25

• 0.50

• 0.88

• 0.12

Why is V not considered a binomial random variable?

• Because the probability of success is not constant

• Because there is no finite number of trials

• Because the trials are not independent

• Because the success metric is not clear

What is the probability that the first four vehicles are not SUVs?

• 0.5997

• 0.88

• 0.7748

• 0.5376

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How is the probability that more than four vehicles are registered before an SUV calculated?

• By adding the probabilities of V being 5, 6, 7, etc.

• By dividing the probability of V being 4 by the probability of V being 5

• By subtracting the probability of V being less than or equal to 4 from 1

• By multiplying the probability of V being 1, 2, 3, and 4

What is the probability that more than four vehicles are registered before an SUV?

• 0.7748

• 0.88

• 0.5997

• 0.12

What does a probability of 59.97% indicate in this context?

• A high chance of registering an SUV first

• A certainty of registering more than four vehicles before an SUV

• A low chance of registering more than four vehicles before an SUV

• A slightly better than half chance of registering more than four vehicles before an SUV

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What is the complement rule used for in this problem?

• To find the probability of registering exactly four vehicles before an SUV

• To find the probability of registering an SUV first

• To find the probability of registering more than four vehicles before an SUV

• To find the probability of registering less than four vehicles before an SUV

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CCSS.HSS.MD.B.6

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