Basic Statistics

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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

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.

  • Basic Statistics -

    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.

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