In the final week of the quiz the Smartest Great Monkey in the World, 6 monkeys are still in the running: the males Choco and Chico and the females Dipsy, Dixie, Dinky and Diggy.
Every day 3 monkeys compete against each other. On the first 3 days, one monkey always falls off and the next day another monkey takes its place. On Thursday, one of the 3 remaining monkeys will win the grand final.
Dipsy, Dixie and Choco start on Monday. Then Dinky (Tuesday), Chico (Wednesday) and Diggy (Thursday) are added as new candidates.
If you know that the 6 monkeys are all equally strong quizzers, what are the chances of a male winning the final?
a) 2/9
b) 20/81
c) 26/81
d) 1/3
e) 1/2
To determine the chances of a male winning the final, we need to consider the number of possible outcomes where a male wins divided by the total number of possible outcomes.
Let's break down the competition day by day to find the possible outcomes:
Day 1:
- Dipsy, Dixie, and Choco compete.
- One monkey falls off, so two remain. Let's say Dipsy falls off.
- Possible outcomes: Choco, Dixie.
Day 2:
- Dixie, Choco, and Dinky compete.
- One monkey falls off, so two remain. Let's say Dixie falls off.
- Possible outcomes: Choco, Dinky.
Day 3:
- Dinky, Choco, and Chico compete.
- One monkey falls off, so two remain. Let's say Chico falls off.
- Possible outcomes: Choco, Dinky.
Day 4 (Grand Final - Thursday):
- Choco, Dinky, and Diggy compete.
- One of them will win the final.
Now, let's calculate the number of outcomes where a male wins:
Outcomes where a male wins: (Choco or Chico)
- Choco wins: Choco, Dixie, Choco (from day 1, day 2, and day 4 respectively).
- Chico wins: Choco, Dinky, Chico (from day 1, day 3, and day 4 respectively).
The total number of possible outcomes: (Choco, Dixie, Choco), (Choco, Dinky, Choco), (Choco, Dixie, Choco), (Choco, Dinky, Choco), (Choco, Dixie, Choco), (Choco, Dinky, Choco) = 6 possible outcomes.
So, the chances of a male winning the final are 2 out of 6 possible outcomes.
Simplifying the fraction, we have 2/6, which can be reduced to 1/3.
Therefore, the answer is d) 1/3.