SOLUTION: A boy found a bicycle lock for which the combination was unknown. The correct combination is a four-digit number. The digits are selected from 1, 2, 3, 5, 6, and 7. a.What is th

Algebra ->  Probability-and-statistics -> SOLUTION: A boy found a bicycle lock for which the combination was unknown. The correct combination is a four-digit number. The digits are selected from 1, 2, 3, 5, 6, and 7. a.What is th      Log On


   

Question 499008: A boy found a bicycle lock for which the combination was unknown. The correct combination is a four-digit number. The digits are selected from 1, 2, 3, 5, 6, and 7.
a.What is the probability that he can open the lock by putting four random numbers in for the combination?
b.What is the probability that he can open the lock at random if he knows that the combination is an odd number?
c.What is the probability that he can open the lock at random if he knows that the numbers in the combination cannot be repeated?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(a)
There are 6 choices for each digit
+6%2A6%2A6%2A6+=+1296+
The boy has a +1%2F1296+ probability of getting
the right combination
(b)
If he knows the number is odd, then the last digit
cannot be 2 or 6, so there are 4
choices for the last digit
+6%2A6%2A6%2A4+=+864+
There is a +1%2F864+ probability of randomly
getting the right odd combination if he knows
the combination is odd
(c)
If numbers can't be repeated
The number of choices are +6%2A5%2A4%2A3+=+360+
There is a +1%2F360+ probability of getting the
right combination if he knows digits can't be
repeated