My son did something quite impressive the other day. It was shear luck but I don't think I'll ever see it duplicated again in my lifetime.
I brought my kids to the boardwalk and my son wanted to play an amusement game. It was the arrow spin wheel game. It had 90 different names or possibilities to win. You could either pick 1 name for \$1 or 3 names for \$2.
He chose 3 names for \$2 and won on his very first try. He picked his prize and we walked over to a completely different spinning wheel game with the same amount of names and cost. On his 1st spin, he won again and again he chose his prize and we left. Yet again we went to a 3rd similar wheel with the same amount of names and chances and he wins again on the 1st try.
What are the odds that someone could win on their 1st 3 tries (or 3 in a row) like my son did? Thanks!
$\endgroup$2 Answers
$\begingroup$With 3 names, the probability to win a game on the first try is $\frac{1}{30}$
So the probability to win 3 games in a row is
$$\frac{1}{30} \times \frac{1}{30} \times \frac{1}{30} = \frac{1}{27000} \simeq 0.003\%$$
If I understand the game correctly, he chose $3$ out of $90$, and so had a $3/90=1/30$ chance in winning a game.
Doing this three times in a row has a probability of $(1/30)^3=1/27000$, so it should happen once in $27000$ tries on average. So, it is pretty unlikely but not excessively so.
$\endgroup$
