Question

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.

Answer 1

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.