Andrew buys a new combination lock for his locker that uses letters instead of numbers. There are five tumblers on the lock, with the letters from A to T on each tumbler.
a) What is the probability that Andrew chooses WATER as the combination?
b) How many possible combinations are there if the letters can be repeated?
c) If it takes 12 seconds to test one combination, how long will it take to check all of the combinations in part b) if Andrew forgets his combination? Express your answer in years and months.
Math help please!!?
2016-06-20 8:48 am
回答 (3)
2016-06-20 10:47 am
look i don t like math ok
2016-06-20 9:02 am
a)
From A to T, there are 20 letters.
There is only 1 letter is chosen for each tumbler.
P(Andrew chooses WATER as the combination)
= (1/20)⁵
= 1/3200000
b)
There are 20 possible letters for each tumbler.
Number of possible combinations
= 20⁵
= 3200000
c)
Time taken
= 12 × 3200000 second
= 12 × 3200000 / (3600 × 24 × 365.25) years
≈ 1.2168 years
≈ 1 year + (0.2168 × 12) months
≈ 1 year 2.6 months
From A to T, there are 20 letters.
There is only 1 letter is chosen for each tumbler.
P(Andrew chooses WATER as the combination)
= (1/20)⁵
= 1/3200000
b)
There are 20 possible letters for each tumbler.
Number of possible combinations
= 20⁵
= 3200000
c)
Time taken
= 12 × 3200000 second
= 12 × 3200000 / (3600 × 24 × 365.25) years
≈ 1.2168 years
≈ 1 year + (0.2168 × 12) months
≈ 1 year 2.6 months
2016-06-20 10:06 am
Totally agree with the answer from 'fooks'.
However, part c needs looking at. You say test all combinations, but surely he will stop when he gets the correct one? Will it take the full 3,200,000 goes to get it right...possibly not.
If it takes 12 seconds to input the combination, then it will take between 12 seconds and 1 year, 2 months, 19 days, 4 hours, 28 mins and 8 secs...to hit on the winning combination.
Not trying to be picky, but giving you something to think about!!
:)>
However, part c needs looking at. You say test all combinations, but surely he will stop when he gets the correct one? Will it take the full 3,200,000 goes to get it right...possibly not.
If it takes 12 seconds to input the combination, then it will take between 12 seconds and 1 year, 2 months, 19 days, 4 hours, 28 mins and 8 secs...to hit on the winning combination.
Not trying to be picky, but giving you something to think about!!
:)>
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