Geometric Distribution Probability Problems

The video tutorial explains geometric distribution through various examples, including rolling a die, spotting a blue car, encountering a teacher, and identifying defective tires. It covers the calculation of probabilities, mean, variance, and standard deviation, and reviews key probability formulas.

What is the probability of getting the first six on the fourth roll of a six-sided die?

• 9.6%

• 8.3%

• 16.7%

• 12.5%

In a geometric distribution, what does the variable 'Q' represent?

• Number of successful events

• Number of trials

• Probability of a failed event

• Probability of a successful event

What is the probability that the seventh car is the first blue car you see?

• 10%

• 15%

• 20%

• 5.7%

If 15% of cars are blue, what is the probability of not seeing a blue car on a single try?

• 85%

• 25%

• 15%

• 75%

What is the probability that the tenth person you encounter in a town is a teacher, given 4% of the population are teachers?

• 4%

• 5%

• 2.77%

• 10%

How do you calculate the mean in a geometric distribution?

• P / Q

• Q / P

• 1 / P

• P * Q

What is the probability that the eighth tire selected has a defect if 2% of tires are defective?

• 3%

• 4%

• 2%

• 1.7%

What is the cumulative geometric distribution function used for?

• Calculating the standard deviation of a distribution

• Calculating the variance of a distribution

• Calculating the mean of a distribution

• Calculating the probability of the first success within a certain number of trials

What is the probability that a defect will be found beyond the 12th sample?

• 78.5%

• 10%

• 25%

• 50%

How do you calculate the standard deviation in a geometric distribution?

• Square root of the variance

• 1 / P

• P * Q

• Q / P