Jen P.

asked • 01/23/21

statistics help!

  1. Your student email account requires you to choose a password of 4 letters followed by one of the digits 0-9. The password can consist of upper case letters (26) or lower case letters (26). How many different five-character passwords can be created? 


The probability of picking the winning 4-digit number in a Pick 4 lottery is 1/10,000. Each play of the lottery is independent of the next play. (a) If you take a very large random sample of purchased lottery tickets, about 0.01% of the tickets will be winners. (True or False?)  

If 10,000 people play the Pick 4 lottery, exactly 1 person will win the lottery. (True or False?)

(c) The winning number in a Pick 4 lottery was 1234 two days in a row, therefore the likelihood of this number being picked again is much lower due to the Law of Averages. (True or False?)



1 Expert Answer

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Jon S. answered • 01/23/21

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52*52*52*52*10 different 5 letter passwords


a) True, if each draw is independent, the probability of each draw is unchanged

b) False, there is 1/10000 probability of winning doesn't mean exactly 1 person will win.

c) False, it is still 1/10000 each draw

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Jen P.

thank you so much! could you tell me how many passwords it would be again? I don't understand your explanation, thank you so much!
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01/23/21

Larry K.

The total number of ways you can do something is the product of the numbers of ways you can do each part. There are 52 different letters, upper and lower case, so you can pick two letters 52 times 52 ways. So for four 4 letters there are 52 times 52 times 52 times 52 ways for a total of 7311616 ways. If you then pick one of ten different numbers, multiply that result by 10. The answer is 73116160 possible passwords.
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01/23/21

Jen P.

thank you so much!
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01/23/21

Jen P.

Thank you very much for your help. I have another question on my account that I really need help with, if you could check that out I would greatly appreciate it. It's the one with no answers. Thank you!
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01/25/21

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