Please give a detailed solution and explanation, thank you! We have a total of 1
ID: 3044407 • Letter: P
Question
Please give a detailed solution and explanation, thank you! We have a total of 100 boxes, all of ... Please give a detailed solution and explanation, thank you! We have a total of 100 boxes, all of which have a dollar bill. For every turn you have, you open a random box and take the bill unless the box is already empty (meaning the bills are not replaced in this scenario). The game is played for n = 50 turns.
1. How likely is that a given box will be opened at least once during a game?
2. What is the expected win?
Explanation / Answer
probability of opening a particular box in a turn =1/100 (as there are 100 boxes)
hence probability of not opening a particular box in a turn =1-1/100 =99/100
a)
probability that a given box will be opened at least once during a game =1-P(it will not get opened in 50 turns)
=1-(99/100)50 =1-0.6050 =0.3950
b) expected win from 1 box =$1 * probability that it gets opened at least>
hence expected win from 100 box =100*0.3950 =$39.50