Geometric or Binomial

About 8% of males are colorblind. A researcher needs some colorblind subjects for an experiment and begins checking potential subjects. 

What’s the probability that the first colorblind man found will be the sixth person checked?

• Binomial

• Geometric

Answer explanation

The scenario describes finding the first success (colorblind man) on the sixth trial, which follows a geometric distribution. Thus, the correct choice is Geometric.

Leo selects 25 grandparents at random from his town to interview. In the town, 35% of the grandparents have their grandchildren living with them. Let G be the number of grandparents Leo interviews whose grandchildren are living with them. What type of variable is G?

• Geometric

• Binomial

• Both

• Neither

Answer explanation

G is a binomial variable because it counts the number of successes (grandparents with grandchildren living with them) in a fixed number of trials (25 interviews), with each trial having two possible outcomes.

The biologist collects and examines a dozen frogs. If the probability of given trait in this species is p, what’s the probability they find the trait in none of the 12 frogs? 

• Binomial

• Geometric

If the probability of given trait in this species is p, how many frogs should they expect to collect before they find one with this trait?

• Binomial

• Geometric

If the probability of given trait in this species is p, what is the probability that the biologist will have to collect no more than 4 frogs before they find one with the trait?

• Binomial

• Geometric

Answer explanation

The question asks for the probability of finding a trait within a certain number of trials. This scenario fits a geometric distribution, which models the number of trials until the first success, making 'Geometric' the correct choice.

What's the probability that at least 3 out of 10 chips need to be rejected?

• Binomial

• Geometric

Answer explanation

The scenario involves a fixed number of trials (10 chips) with two possible outcomes (reject or not reject). The probability of rejection is constant (2%). Thus, this follows a Binomial distribution.

What’s the probability you find 1 bad one within the first 10 you examine?

• Binomial

• Geometric

Answer explanation

The scenario describes a fixed number of trials (10 chips) with two outcomes (bad or good). The probability of finding 1 bad chip follows a binomial distribution, making 'Binomial' the correct choice.

About 8% of males are colorblind. A researcher needs some colorblind subjects for an experiment and begins checking potential subjects. 

On average, how many men should the researcher expect to check to find one who is colorblind?

• Binomial

• Geometric

Answer explanation

The situation describes a scenario where we are looking for the first success (finding a colorblind man) in a series of independent trials. This follows a geometric distribution, where the expected number of trials to get one success is 1/p, with p being the probability of success (0.08).

About 8% of males are colorblind. A researcher needs some colorblind subjects for an experiment and begins checking potential subjects. 

What’s the probability that they won’t find anyone color-blind among the first 4 men they check?

• Binomial

• Geometric

Answer explanation

The scenario involves checking a fixed number of subjects (4 men) for a specific outcome (colorblindness). The probability of not finding a colorblind man follows a binomial distribution, making 'Binomial' the correct choice.

About 8% of males are colorblind. A researcher needs some colorblind subjects for an experiment and begins checking potential subjects. 

What’s the standard deviation of the number of people that they need to check to find the first one who's colorblind?

• Binomial

• Geometric

Answer explanation

The scenario describes finding the first colorblind male, which follows a geometric distribution. The standard deviation for a geometric distribution is calculated as (1-p)/p, where p is the probability of success (0.08). Thus, the correct choice is Geometric.