Geometric Probability

Front

What is Geometric Probability?

Back

Geometric Probability is a type of probability that deals with the likelihood of an event occurring in a continuous space, often involving lengths, areas, or volumes.

Front

What is the formula for calculating the probability of the first success on the k-th trial in a geometric distribution?

Back

P(X = k) = (1 - p)^(k-1) * p, where p is the probability of success.

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What is the difference between Geometric and Binomial distributions?

Back

Geometric distribution models the number of trials until the first success, while Binomial distribution models the number of successes in a fixed number of trials.

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What is the probability of not running a red light until the 6th drive if the chance of running a red light is 40%?

Back

0.03 (calculated using the geometric distribution formula).

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What does it mean for events to be independent in probability?

Back

Events are independent if the occurrence of one event does not affect the probability of the other event occurring.

Front

What is the probability of rolling a 6 for the first time on the 6th roll of a die?

Back

Geometric distribution is used because we are looking for the first success after a certain number of trials.

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What is a Binomial Distribution?

Back

A Binomial Distribution is a probability distribution that summarizes the likelihood that a value will take one of two independent states and is defined by the number of trials and the probability of success.

Front

What is the probability of exactly 2 out of 20 blood donors having Type B blood if the probability of having Type B blood is 11%?

Back

0.282 (calculated using the binomial distribution formula).

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What is the significance of the number of trials being fixed in a Binomial Distribution?

Back

In a Binomial Distribution, the number of trials must be fixed to determine the probability of a certain number of successes.

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What does it mean for a distribution to be approximately symmetric?

Back

A distribution is approximately symmetric if the left and right sides of the distribution are mirror images of each other.