In each of the following situations state whether or not the given assignment of probabilities to individual outcomes is legitimate, that is, satisfies the rules of probability. If not, give a reason

a) roll a die and record the count of spots on the up-face
P(1)=0 P(2)=1/6 P(3)=1/3 P(4)=1/3 P(5)=1/6 P(6)=0

b) Deal a card from a shuffled deck:
P(clubs)=12/52 P(diamonds)=12/52 P(hearts)= 12/52 P(spades)=16/52

c) Choose a college student at random and record sex and enrollement status
P(female full time)=0.56 P(male full time)=0.44
P(female part time)=0.24 P(male part time)= 0.17

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If I am right, A would not be legitimate since each number on the die has an equal chance of being rolled, meaning each should be 1/6. I saw a similar problem to it, but it says it is legitimate. I don't know what to think.

I do believe its obvious that B is not legitimate. All types of cards should be 13/52

And for C, I do believe its legitimate.

I'm worried I'm off track. Thanks for the help.

I agree with you about A. Each number of spots has p = 1/6. I bet your other problem had two dice.

Agree - obvious because spades may not be different from other suits.

.56 + .44 + .24 + .17
is more than one, since there is no overlap (intersections if you drew a Venn diagram) that is impossible.

You are on the right track with your analysis. Let's go through each situation to determine if the given assignment of probabilities is legitimate.

a) Roll a die and record the count of spots on the up-face.
P(1)=0, P(2)=1/6, P(3)=1/3, P(4)=1/3, P(5)=1/6, P(6)=0.

In this case, you correctly identified that each number on the die should have an equal chance of being rolled, which is 1/6. However, note that the probabilities given for each number must add up to 1. In this situation, the probabilities of rolling a 2, 3, 4, and 5 add up to 1, but the probabilities for rolling a 1 and 6 are both 0. Therefore, the given assignment of probabilities is not legitimate because it doesn't satisfy the rule that probabilities must sum up to 1.

b) Deal a card from a shuffled deck.
P(clubs)=12/52, P(diamonds)=12/52, P(hearts)=12/52, P(spades)=16/52.

You correctly pointed out that all types of cards should have an equal chance of being dealt, which is 1/4 since there are four suits. However, the probabilities given do not add up to 1. The total probability should be 1 since you will always deal a card from the deck. Therefore, the given assignment of probabilities is not legitimate.

c) Choose a college student at random and record sex and enrolment status.
P(female full time)=0.56, P(male full time)=0.44, P(female part time)=0.24, P(male part time)=0.17.

For this situation, the given probabilities seem to be legitimate. The probabilities provided are non-negative and they sum up to 1, which satisfies the properties of probability. Therefore, the given assignment of probabilities is legitimate in this case.

In summary, the correct assessments are as follows:
a) The given assignment of probabilities is not legitimate.
b) The given assignment of probabilities is not legitimate.
c) The given assignment of probabilities is legitimate.