If there is a slot machine with 4 slots, each with a possibility of being either a cherry, a lemon, or a 7, what is the probability of getting exactly two lemons?
My thinking:
4 slot machine, 3 options: 3*3*3*3 = 81 total options.
getting exactly 2 lemons: 1*1*3*3 = 9
P(LL) = 9/81 = 0.1111
What is wrong with this?
Best Answer
Your calculation assumes that lemons must be in the first two slots (the $1$s you multiply in) and allows lemons in the last two slots (the $3$s you multiply in), so would accept four lemons and reject 7-7-lemon-lemon. You should compute the number of ways to choose the two slots for the lemons, then require that the other two slots be non-lemons.