I don't agree with their answer . . .
Aki is a participant on a trivia-based game show. He has an equal likelihood on any
given trial of being asked a question from one of six categories: A, B, C, D, E, or F.
Aki feels that he has an 50% chance of getting an A or B question correct,
but he thinks he has a 90% probability of getting any of the other questions right.
If Aki has to get two of three questions correct, what are his odds ? of winning?
The answer is 43/50 . . . . . This is not odds!
The probability of getting an A or B question is: .
The probability of answering an A or B question correctly is: .
. . Hence, the probability of answering an A or B question correctly is: .
The probability of getting an Other question is: .
The probability of getting an Other question correct is: .
. . Hence, the probability of answering an Other question correctly is: .
So the probability of answering any question correctly is: .
. . The probability of getting it wrong is: .
There are two ways that Aki can win . . .
(1) His first two answers are Right.
(2) He answers the first one wrong, and one of the last two right.
Therefore, his probability of winning is: .
His odds of winning are approximately