Amy, Brenda, Charles and Darren are playing treasure hunt in the garden. There are 100 boxesnumbered from 1 to 100 located at 100 different locations in the garden. Afterthe treasure hunt,Amy goes home and realizes she has lost her key. So, she phones her friends who are still inthe garden to search for the lost key before she gets back to the garden. Since the treasure hunthas ended, all the boxes are opened. Brenda finds that all the even-numbered boxes do notcontain the key, so she closes these boxes. Charles changes the status of the boxes whichnumbers are multiple of 5 (if it is open, closes it or vice versa). Darren repeats the action ofSeleCharles but the boxes he changes are the boxes which numbers are multiple of7.What is the probability that Amy will get her key back in the opened boxes?Brenda =charles

Answered: Amy, Brenda, Charles and Darren are…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter14: Counting And Probability

Section14.1: Counting

Problem 92E

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Question

Amy, Brenda, Charles and Darren are playing treasure hunt in the garden. There are 100 boxes
numbered from 1 to 100 located at 100 different locations in the garden. Afterthe treasure hunt,
Amy goes home and realizes she has lost her key. So, she phones her friends who are still in
the garden to search for the lost key before she gets back to the garden. Since the treasure hunt
has ended, all the boxes are opened. Brenda finds that all the even-numbered boxes do not
contain the key, so she closes these boxes. Charles changes the status of the boxes which
numbers are multiple of 5 (if it is open, closes it or vice versa). Darren repeats the action of
Sele
Charles but the boxes he changes are the boxes which numbers are multiple of7.
What is the probability that Amy will get her key back in the opened boxes?
Brenda =
charles

Expert Solution

Step 1

Given:

The total number of boxes is 100, which is numbered from 1 to 100 placed at different locations in garden. Amy lost her key at the end of treasure hunt and Brenda finds that even numbered boxes do not have keys. The probability that Amy will get her key in opened boxes has to be calculated.

Step 2

To find the probability that Amy will get key in opened boxes as follows,

Total number of boxes = 100

Since even-numbered boxes are checked, number of remaining boxes = 50

It is given that all the boxes are opened at the end of treasure hunt. So, Darren and Charles close the boxes which are multiples of 7 and 5 respectively.

Closed boxes indicate that check is not required because girls consider those boxes were not opened during hunt. Hence, those boxes donot have chance of having key.

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