Assignment on What is Probability Explain?.

Probability 1
PROBABILITY
by Student’s Name
Code + Course Name
Professor’s Name
University Name
City, State
Date
Probability

Probability 2
1. Coin Flips
A – heads atleast 4
B – heads equal to tails = 3
C – consecutive 4 heads
Pr ( H ) =1
2 ∧Pr ( T ) =1
2
Pr ( A )=Pr ( HHHH )∨Pr ( HHHHH )∨Pr ( HHHHHH ) orPr ( HHHHT ) orPr ( HHHHTT ) orPr ( HHHHTH )
¿ 1
24 + 1
25 + 1
26 + 1
25 + 1
26 + 1
26
¿ 11
64
Pr ( B ) =Pr ( HHH ) =Pr ( TTT )
¿ 1
2
3
= 1
8
Pr ( C )=Pr ( HHHH )
¿ ( 1
2 ) 4
= 1
16
Pr ( A /B ) = Pr ( A ) Pr ( A ∩B )
Pr ( B )
¿
11
64 × 1
8
1
8
¿ 11
64
Pr (C / A)= Pr ( C ) Pr ( C ∩ A )
Pr ( A )

Probability 3
¿
1
16 × 1
16
11
64
= 1
44
2. Probability of 5 before 7
A – d1 + d2 = 7
B – d1 + d2 = 5
C - A ∪ B
Pr ( 1 , ... , 6 )= 1
6
The first appearance of A = 1 and 6 or 2 and 5 or 3 and 4 or 4 and 3
While first appearance of B = 1 and 4 or 2 and 3 or 3 and 2 or 4 and 1
A ∪ B=(1,6)(1,5)(1,4)(2,3)(2,4)(2,5)(3,2)(3,3)(3,4)(4,1)( 4,2)( 4,3)
Pr ( A ) = 1
36 + 1
36 + 1
36 + 1
36 = 1
9
Pr ( B ) = 1
36 + 1
36 + 1
36 + 1
36 = 1
9
Pr ( C )= 12
36
Pr ( C ∩ A )= 4
36
Pr (A /C)= Pr ( A)Pr ( C ∩ A )
Pr (C)
¿
1
9 × 1
9
12
36
= 1
27
3. Four-Door Monte Hall