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Dafna11 [192]
3 years ago
6

Thief steals an atm card and must randomly guess the correct threethree?-digit pin code from a 99?-key keypad. repetition of dig

its is allowed. what is the probability of a correct guess on the first? try?
Mathematics
1 answer:
Zielflug [23.3K]3 years ago
3 0
We are given a key pad assuming that the numbers are of 10 options from 0 to 9. IN thsi case, guessing the 3 digit pin number can be determined via counting method. The first number has 10 options so as second and third. Hence the total number of options is 10^3 or 1000. The probability of getting the pin teh first time is 1/1000 or 0.001. 
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Answer:

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And the anfle is approximately \theta \approx 48

Step-by-step explanation:

For this case first we need to calculate the dot product of the vectors, and after this if the dot product is not equal to 0 we can calculate the angle between the two vectors in order to see if there are parallel or not.

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The dot product on this case is:

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Since the dot product is not equal to zero then the two vectors are not orthogonal.

Now we can calculate the magnitude of each vector like this:

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|b| =\sqrt{(4)^2 +(0)^2 +(-3)^2}=\sqrt{25}= 5

And finally we can calculate the angle between the vectors like this:

cos \theta = \frac{ab}{|a| |b|}

And the angle is given by:

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If we replace we got:

\theta = cos^{-1} (\frac{10}{\sqrt{9} \sqrt{25}})=cos^{-1} (\frac{10}{15}) = cos^{-1} (\frac{2}{3}) = 48.190

Since the angle between the two vectors is not 180 or 0 degrees we can conclude that are not parallel

And the anfle is approximately \theta \approx 48

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