Question

Which of the following random variables is geometric?

Question 4260 Options (Mathematics):
A) The number of 5s when rolling a die 35 times.
B) The number of spades dealt from a shuffled deck of 52 cards in a seven-card hand.
C) The number of heads when a coin is tossed 10 times.
D) The number of digits in a randomly selected row until a 9 is found.
E) The number of 8s in a row of 20 random digits.

Answer 1

The random variable that is geometric among the options provided is D) The number of digits in a randomly selected row until a 9 is found. It corresponds to the definition of a geometric distribution where we count the number of independent trials until the first success.

Step-by-step explanation:

Understanding Geometric Distribution

A random variable is said to have a geometric distribution if it models the number of trials until the first success in a sequence of independent and identically distributed Bernoulli trials (each with a success probability p). The question asks us which of the random variables listed is geometric.

Option D) The number of digits in a randomly selected row until a 9 is found represents a geometric situation because we're interested in the number of trials (digits) until the first success (finding a 9). Each digit has an independent probability p (1/10 if we assume that each digit from 0 to 9 is equally likely) of being a 9. We continue checking digits until we first encounter a 9.

Summary of the Geometric Distribution

• Random Variable X: The number of trials until the first success.
• Distribution of X: X ~ Geom(p), where p is the probability of success on each trial.
• Possible Values of X: Positive integers starting from 1 (1, 2, 3, ...).