The Discrete Mathematics

Running head: Discrete Mathematics
Discrete Mathematics
Name of the Student
Name of the University

Discrete Mathematics2
Q1.
Coin Flips
The size of the sample space when a coin is flipped six times: 26
1.
Pr(A) = 6 C 4 +6 C 5+6 C 6
26 =15+ 6+1
64 = 22
64 = 11
32
2
Pr(B) = 6 C 3
26 = 20
64 = 5
16
Four consecutive heads can occur in 3 ways. Five consecutive heads can occur in 2 ways.
And six consecutive heads can occur in 1 way.
3.
Pr ( C ) = 3+2+1
64 = 3
32
4.
Pr (A|B) = 0.
5.
Pr( C|A) = (3+2+1 ¿/¿) = 6/22 = 3/11
2.
Probability of 5 before 7
The number 5 can appear in the following ways when two dice are rolled together
: (1, 4), (2, 3), (3, 2), (4, 1)

Discrete Mathematics3
Pr(A) = 4/36 =1/9
The number 7 can appear in the following ways: (1,6), (6,1), (2,5), (5,2), (3,4), (4,3)
Pr(B) = 6/36 =1 / 6
Probability that neither 5 or 7 appears: 1 – (1/9 +1/6) = 1 – 15/54 = 1 – 5/18 = 13/18
A five can be rolled before a seven in the following ways:
A five is rolled on the first roll: Probability: 1/9
A five is rolled on the second roll preceded by neither 5 nor 7 in the earlier rolls: (13/18)*
(1/9)
A five is rolled on the third roll preceded by neither 5 nor 7 in the earlier two rolls:
( 13
18 )2
∗( 1
9 )
Thus adding all such possible ways we get an infinite geometric series:
1
9 + ( 13
18 )∗( 1
9 ) + ( 13
18 )
2
∗( 1
9 ) +... ....=
1
9
1−13
18
=
1
9∗18
5 = 2
5
3. Four-Door Monte Hall
1. Probability that I win the sports car remains the same if I go with the first choice: (1/4)
2. Probability that I win the sports car by opening one of the three unopened doors at
random: (1/3)