Question

Geometric or not? Determine whether each of the following scenarios describes a geometric setting. If so, define an appropriate geometric random variable.

a. A popular brand of cereal puts a card bearing the image of 1 of 5 famous NASCAR drivers in each box. There is a $1/5$chance that any particular driver's card ends up in any box of cereal. Buy boxes of the cereal until you have all 5 drivers' cards.

b. In a game of 4-Spot Keno, Lola picks 4 numbers from 1 to 80 . The casino randomly selects 20 winning numbers from 1 to 80 . Lola wins money if she picks 2 or more of the winning numbers. The probability that this happens is \(0.259\). Lola decides to keep playing games of 4-Spot Keno until she wins some money.

Short answer

(a)No geometric distribution, the reason is that does not count until the first success and interested in five successes.

(b) the reason is that the two possible results are win money and do not win money, draws are independent and compute the number of draws until the first success and $p=0.259$.

Step-by-step solution

Part (a) Step 1: Given Information

The following examples describe whether or not a geometric setting exists. If so, define an appropriate geometric random variable.

Part (a) Step 2: Simplification

The geometric distribution of a random variable When a variable has two possible outcomes, each draw is independent of the previous ones. The variable computes the number of draws needed until the first success. Every draw has the same chance of winning.

There is no geometric distribution because it does not count until the first success and is only interested in five successes.

Part (b) Step 1: Given Information

The following examples describe whether or not a geometric setting exists. If so, define an appropriate geometric random variable.

Part (b) Step 2: Simplification

The geometric distribution of a random variable When a variable has two possible outcomes, each draw is independent of the previous ones. The variable computes the number of draws needed until the first success. Every draw has the same chance of winning.

Every draw has the same chance of winning.

The reason for this is that the two possible outcomes are win money and do not win money, drawings are independent, and the number of draws until the first success is computed.

$p=0.259$.