What does a discrete probability distribution list?

• every value the variable can take, with the chance of each
• the outcomes of the experiment in the order they happened
• the average value of the random variable over many trials
• the number of times that each outcome came up during an experiment

The probabilities of all possible values in a discrete probability distribution always add up to 1.

Two fair six-sided dice are rolled independently. Why is each of the 36 ordered face pairs equally likely?

• because there are more pairs than there are totals to spread them over
• because every total from 2 to 12 has the same chance of coming up
• because the dice are rolled at the same moment
• because each die is fair and the two rolls do not affect each other

A coin is flipped three times and X is the number of heads. How many of the 8 equally likely outcomes give X = 2?

• 2
• 3
• 4
• 6

A distribution's probabilities add to 0.9. What does that tell you?

• that the random variable is more likely to be small than large
• that a value has been left out, or one of the entries is wrong
• that the remaining 0.1 belongs to the largest value in the list
• that the experiment has to be repeated ten more times to fix it

A distribution lists values 0, 1, 2 and 3 with probabilities 0.1, 0.35, 0.3 and one missing. What is P(X ≥ 2)?

For two fair dice rolled independently, how do the theoretical probabilities differ from the relative frequencies in 36 rolls?

• The model gives chances; observed frequencies record one run
• The experiment changes the model probabilities after each roll
• Every total must occur equally often in any run of 36 rolls
• The model and observed frequencies must always disagree

For the number of heads X in three flips, P(0) = 1/8, P(1) = 3/8, P(2) = 3/8 and P(3) = 1/8. What is P(X ≥ 2)? Give a decimal.

A distribution lists values 1, 2 and 3 with probabilities 0.4, 2k and k. What is k?

Dee has only a distribution of the total of two six-sided dice. Total 6 has positive probability, but individual face-pair probabilities are unknown. What can she conclude about the chance of a double from this table alone?

• 6 / 36, reading it straight off the entry for the total of 7 in the finished table
• 1 / 36, since only a double six would count as a double in this particular game
• the table cannot separate doubles from non-doubles with the same total
• 0, because the absence of a separate doubles entry means every matching pair has probability zero