Amy, Brenda, Charles and Darren are playing treasure hunt in the garden numbered from 1 to 100 located at 100 different locations in the garden. After the 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 Charles but the boxes he changes are the boxes which numbers are multiple of 7. Bren What is the probability that Amy will get her key back in the opened boxes? Char
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.
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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