Mercy has purchased a BMW 760i. She puts its key into one of the 3empty boxes: b
ID: 3176448 • Letter: M
Question
Mercy has purchased a BMW 760i. She puts its key into one of the 3empty boxes: box 1, box 2, and box 3. She has closed all the boxes, so you do not know which box has the key. She will give you the new car if you select the box that contains thekey. You select box 1 but do not open it. Of the remaining 2 boxes, she opens the box that doesnot have the key. She opens box 3. She gives you the option of replacing your box 1 with box 2.
a. Calculate the probability that box 1 contains the key .
b. Calculate the probability that box 2 contains the key.
use a tree diagram with the following events.
Ak = box k contains key
Bk = Mercy opens box k
At the root of the tree is the event that you select box 1.
Explanation / Answer
a) probability that box 1 contains the key . = 1/3
b) the probability that box 2 contains the key. = 2/3
This is famous Monty Hall problem .
You can go to
http://mathforum.org/dr.math/faq/faq.monty.hall.html