Homework 2
Due on Friday, May 30, 11am.
For each problem just giving the answer will not suffice; a proper argument is
required.
Problem 1
A lock on a lab door has buttons numbered 0 through 9.
The right code for
opening the lock is 8542. Also, if on three consecutive attempts, a wrong code
(a code is a combination of 4 ordered distinct digits) is entered, then a burglar
alarm is let off.
Anna forgot the right code, but remembers that the code
consists of 4 distinct digits.
So she keeps on trying one code after another
without replacement. Compute the probability that she gets in (without letting
off the alarm). Please report the answer in
p
q
form, it’s OK to not simplify.
Solution
Total number of codes (
ie
, ordered combination of 4 distinct digits)
=
10
·
9
·
8
·
7
=
5040
No. of ways in which Anna will NOT get the correct code in the three trials
= 5039
·
5038
·
5037
Thus, probability of Anna’s getting in
=
1

5039
·
5038
·
5037
5040
·
5039
·
5038
=
1

5037
5040
=
3
5040
=
1
1680
Problem 2
An urn contains 10 Red and 5 black balls. Two balls are picked (one after the
other) from the urn.
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 Summer '07
 EHRLICHMAN
 Playing card, Card game, pinochle deck

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