I'm not feeling very confident with probabilities so I would like some confirmation of my answers if possible. Thanks in advance!
The security code needed to open a safe in a jewellery shop is 590821. A burglar tries to open the safe by entering a randomly chosen sequence of 6 digits (where each digit entered is equally likely to be any integer from 0 to 9, independently of all other digits).
a) Find the probability that the burglar gets the first or the last digit right (or both).
Using the equation:
*# of sample points in Event / Total # of sample points
# of sample points in Event is = 3 because we want the First digit, last digit or both totalling 3.
Total # of sample points = 10 x 10 = 100 because we are dealing with only 2 parts of the lock.
So for a) 3/100 ? is this correct?
(b) Find the probability that the burglar enters the correct code.
Total # of sample points = 10 x 10 x 10 x 10 x 10 x 10 = 100,000 # of sample points = 6
so 6/100,000 for part b?
(c) Find the probability that the burglar gets exactly two of the six digits right.
A little more tricky, when calculating the #sample of points. Not sure how to do this one. But I think we need to think about how many ways we can get 2 digits correct out of the 6 digits. So 6C2 = 6!/2!(6-2)!
so 8.6 / 100,000 for part c?
(d) Given that the burglar gets exactly two of the six digits right, find the probability that the first two digits are wrong.
not sure how to answer this.