Answer:
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