The game has 5 colors red yellow green blue and black
A player randomly picks 4 colors and sorts them in a line the second player has to guess how the first player sorted them.
- Mike picked and sorted four random colors (the color can be used more than once) what is the probability of guessing it right from the first try?
since Mike has to guess it right from the first time it is going to be $\frac {1} {n(Ω)}$ and our $n(Ω)$ is $5*5*5*5$ since we have 5 colors and each color can be used more than once so my answer was $\frac {1} {5^4}$
- Julia knows that the color yellow appears atleast once what is the probability she guesses it right from the next guess try? (the answer should be $\frac {1} {369}$ according to the book
what I tried was $n(Ω)$=${4 \choose 1}$ $*$ $5*5*5$ but this is wrong and it felt more like guessing to me and I also could not figure out what they mean by "next try" does it mean she tried 2 times or just once?
- Mike told Julia that in his order no color appears more than once what is the probability that Julia gets it right from the first try?
What I tried was $\frac {1} {5*4*3*2}$ and it also seems to be right according to the book.
Much appreciation for any help and tips on the 2nd question and if anyone can confirm that the 1st and 3rd questions are right. thank you
Best Answer
The first and third answers look correct on the assumption all possible patterns in order are equally likely.
A hint for the second question:
Consider the number of patterns which do not include any yellows, i.e. the number selecting from red, green, blue and black. Then subtract this number from the overall number of possible patterns (your answer to the first question) to give the number of patterns in which yellow appears at least once.