Unit 2 Probability Thread

[dinosaur93]

pls cross check whether or not its approached the right way! tnx!

Mike needs to randomly guess a password.
Extrapolated from the riddle, He was also to obtain that the password is 5 characters long. At the same time, the password was restricted to 70 possibilities for each character

• 26 lowercase,
• 26 uppercase,
• 10 digits and
• 8 symbols

Question 1
Write an expression for how many different passwords could be randomly generated?

 

***This is definitely a combination yeah?



Question 2
If Mike's computer was able to generate a total of 100 guesses per second, then how long will it take him to solve the riddle (and crack the password)? Mike knew that it would take days for him to solve the riddle therefore wishes to round it to the nearest day. 




This is taking too long for Mike to solve the riddle. After crosschecking it again with his friend, He was further given another hint. That the first four characters of the password are definitely letters, but the last character is a number or symbol.

Question 3
How many different combinations of password can Mike generate knowing that the first four characters are letter and the last characters is a number of symbol?



Question 4
Using this assumption, How long will it take Mike to solve the riddle? Is it faster than the first scenario, if so, by how many days?

[brightsky]

q1: it's a permutation since order matters.
q2: you should have 70^5/(100*60*60*24) =194.52..=195 days .
q3: (26*26)^4*10*8. use box method. don't use combinations unless you absolutely have to and/or it assists your thought process.
q4: ((26*26)^4*10*/(100*60*60*24) = 1.933... = 2 days. much faster than first scenario...by 193 days.

[dinosaur93]

Could you pls elaborate question 3 again, I didnt quite get that, thank you! 

[dinosaur93]

Question 1
Suppose you play a game of cards in which only three cards are dealt from a standard 52-card deck. How many ways are there to obtain one pair? (2 cards of the same rank and 1 card of a different rank.)


Question 2
Consider the four events shown below involving randomly drawing a card from a standard deck of 52 cards. Which of the events are mutually exclusive?
F: the card is a face card
K: the card is a King
S: the card is a spade
H: the card is a heart

A.  F and H                B.  F and K                 C.  S and H                  D.  S and K

[brightsky]

1) 13*4C2*48C1/52*3
2) C (mutually exclusive means they can't happen at the same time)