The following distribution table represents preferences for two types of cereals by 2000 boys and girls. Determine the probability that the person is a boy, given that the person likes Fruity Cereal.
A) 500/1,000
B) 500/2,000
C) 1,200/2,000
D) 500/1,200

Question

The following distribution table represents preferences for two types of cereals by 2000 boys and girls.  Determine the probability that the person is a boy, given that the person likes Fruity Cereal.
A) 500/1,000 
B) 500/2,000 
C) 1,200/2,000 
D) 500/1,200

Quizplus · Accepted Answer

We need to find the probability of a person being a boy given that they like Fruity Cereal. We can use Bayes' theorem:

P(Boy | Fruity) = P(Fruity | Boy) * P(Boy) / P(Fruity)

P(Fruity) can be found by summing the number of people who like Fruity Cereal, regardless of gender:

P(Fruity) = (500 + 700) / 2000 = 1.2/2 = 0.6

P(Fruity | Boy) is the proportion of boys who like Fruity Cereal:

P(Fruity | Boy) = 500/1000 = 0.5

P(Boy) is the proportion of boys in the sample:

P(Boy) = 1000 / 2000 = 0.5

Now we can substitute these values into Bayes' theorem:

P(Boy | Fruity) = 0.5 * 0.5 / 0.6 = 0.4166

So the probability that the person is a boy, given that they like Fruity Cereal, is approximately 0.4166 or 500/1200. Therefore, the best choice is D, 500/1,200.

The Following Distribution Table Represents Preferences for Two Types of Cereals