Question

In each of the situations, choose whether or not the given assignment of probabilities to individual outcomes is legitimate. Remember, a legitimate model need not be a practically reasonable model. If the assignment is not legitimate, choose the correct reason for your answer.

(a) Roll a six‑sided die and record the count of spots on the up‑face:

?(1)=0,?(2)=1/6,?(3)=1/3,?(4)=1/3,?(5)=1/6,?(6)=0P(1)=0,P(2)=1/6,P(3)=1/3,P(4)=1/3,P(5)=1/6,P(6)=0 .

This is not a legitimate model because the sum of the probabilities does not equal 11 .

This is not a legitimate model because you cannot have a probabiltiy of 00 .

This is a legitimate model.

This is not a legitimate model because one of the probabilities is greater than 11 .

(b) Deal a card from a shuffled deck:

?(clubs)=12/52P(clubs)=12/52 ,  ?(diamonds)=12/52P(diamonds)=12/52 , ?(hearts)=12/52P(hearts)=12/52 , ?(spades)=16/52P(spades)=16/52 .

This is a legitimate model.

This is not a legitimate model because you also need to consider the probability of the face cards.

This is not a legitimate model because the sum of the probabilities does not equal 11 .

This is not a legitimate model because one of the probabilities is greater than 11 .

(c) Choose a college student at random and record sex and enrollment status:

?(female full‑time)=0.56,?(female part‑time)=0.24,?(male full‑time)=0.44,?(male part‑time)=0.17P(female full‑time)=0.56,P(female part‑time)=0.24,P(male full‑time)=0.44,P(male part‑time)=0.17 .

This is not a legitimate model because the sum of the probabilities is greater than 11 .

This is not a legitimate model because you cannot combine the probability of sex and enrollment status.

This is a legitimate model.

This is not a legitimate model because one of the probabilities is greater than 11 .

Answer 1