Question

Which of the following random variables is geometric?

The number of 1s when rolling a die 25 times
Ob
The number of digits in a randomly selected row until a 3 is found
Ос
The number of queens dealt from a shuffled deck of 52 cards in a seven-card hand
Od
The number of tails when a coin is tossed 50 times
The number of 4s in a row of 30 random digits

Answer 1

The random variable geometric is the one that represents the number of digits in a randomly selected row until a 3 is found since it fits the characteristics of a geometric experiment - the process stops after the first success and each trial has an equal chance of success.

Step-by-step explanation:

The random variable that is geometric is the number of digits in a randomly selected row until a 3 is found. A geometric distribution is defined as a discrete random variable that arises from the Bernoulli trials; the trials are repeated until the first success. The geometric variable X is defined as the number of trials until the first success, with each trial being independent and having the same probability of success.

In the scenario of rolling a die 25 times or tossing a coin 50 times, these are not geometric because they do not fit the definition of stopping after the first success. Similarly, dealing a specific number of cards from a shuffled deck does not fit the geometric definition, as it involves a fixed number of trials. In contrast, the question about finding the number of digits until a 3 is located fits the criteria because the process stops once the first 3 is observed, and each digit has an equal and independent chance of being a 3.

Answer 2

b. The number of digits in a randomly selected row until a 3 is found.

Step-by-step explanation:

A random variable often used in statistics and probability, is a variable that has its possible values as numerical outcomes of a random experiment or phenomenon. It is usually denoted by a capital letter, such as X.

In statistics and probability, random variables are either continuous or discrete.

1. A continuous random variable is a variable that has its possible values as an infinite value, meaning it cannot be counted.

2. A discrete random variable is a variable that has its possible values as a finite value, meaning it can be counted.

Also, any random variable that meets certain conditions defined in a research study.

Hence, an example of a geometric random variables is the number of digits in a randomly selected row until a 3 is found.