On the trivia game show Jeopardy, three contestants select from a board of 30 clues; each clue is assigned a monetary value. Each correct answer adds to a contestant’s monetary score, an incorrect answer results in a decrease in the score. A Daily Double is assigned to a clue or two on the board. A clue with a Daily Double allows the contestant to determine the monetary value up to the current score.
a. In the first round of the game show, 1 of the 30 clues is a Daily Double. What is the probability that a contestant finds the Daily Double on the first selection?
b. Given that 15 clues have been selected in the first round without a Daily Double, what is the probability a contestant finds the daily double?
c. The probabilities in parts (a) and (b) are conditional probabilities. What is the conditional common to each?
d. In the second round of Jeopardy, Daily Doubles are assigned to 2 of the 30 clues. On the first selection, what is the probability of finding a daily double?
e. In the second round, suppose that 15 clues were selected, and not one was a Daily Double. What is the probability a contestant finds a Daily Double?
f. The probabilities in parts (d) and (e) are conditional probabilities. What is the condition common to each?