Question

There are three clues labeled "daily double" on the game show Jeopardy. If three equally matched contenders play, what is the probability that: a. A single contestant finds all three "daily doubles"? b. The returning champion gets all three of the "daily doubles"? c. Each of the players selects precisely one of the "daily doubles"?

Answer 1

a) 0.0358

b) 0.0395

c) 0.1506

Step-by-step explanation:

Number of clues "daily doubles" = 3

Determine the probabilities

a) P(single contestant finds all three )

assuming event A= a returning champion gets the "daily double" in first trial

P(A) = 1/30 , P(~A) = 29/30

assuming event B = any player picks up "daily double" after the first move

P(B |~A ) = 1/3

hence : P ( B and ~A ) = 29/30 * 1/3 = 29/90

considering second round

P(player chooses both daily doubles ) = 1/3 * 1/3 = 1/9

∴ P(single contestant finds all three ) = 29/90 * 1/9 = 0.0358

B) P ( returning champion gets all three )

= (1/30 + 29/90 )* 1/9

= 32 / 810 = 0.0395

c) P ( each player selects only one )

P = 32/405 + 29/405

= 61 / 405 = 0.1506