So here goes the question:
I've approached this question with the presumption that the two events are independent. For the magician to have even considered putting his hand in the green hat; there had to be a sum of 4 or less produced by the rolling of the two dice.A magician has two hats containing flowers and animals.
The black hat has 3 roses and 2 bunnies.
The green hat has 5 roses and 3 bunnies.
A volunteer from the audience rolls two standard dice (numbers 1 to 6). If the sum of the numbers is equal to or less than 4, the magician takes an object out from the green hat; otherwise the magician takes an object from the black hat.
If the magician obtains a bunny,
what is the probability that it came from the green hat?
I calculated the chance of rolling sum of 4 or less to be: 6/36 = 0.1666
The chance that a bunny is pulled out can be calculated by: 3/8 = 0.375
adding the above two values reveals the probability to be : 0.5416
What do you guys think? If my reasoning flawed? Are these mutually dependent events? Any insight would be greatly appreciated!