Monkeys

Mar 2020
20
0
Netherlands
In the final week of the quiz "the Smartest Great Monkey in the World", 6 monkeys are still in the running: (male) Choco and Chico and (females) Dipsy, Dixie, Dinky and Diggy.

Every day 3 monkeys compete against each other. In 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

the answer has to be 1/3 but I don't know how. Can someone pls explain it
 

romsek

Math Team
Sep 2015
2,958
1,673
USA
Sim shows p = 26/81

So does counting the male leaf nodes of the tree.

Work it through.
 
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