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Assignment about What is Probability?

   

Added on  2022-09-15

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Probability 1
PROBABILITY
by Student’s Name
Code + Course Name
Professor’s Name
University Name
City, State
Date
Assignment about What is Probability?_1

Probability 2
Probability
1. Coin Flips
A – heads atleast 4
B – heads equal to tails = 3
C – consecutive 4 heads
Pr(𝐻) = 1
2 𝑎𝑛𝑑 Pr(𝑇) = 1
2
Pr(𝐴)
= 𝑃𝑟(𝐻𝐻𝐻𝐻) 𝑜𝑟 𝑃𝑟(𝐻𝐻𝐻𝐻𝐻)𝑜𝑟 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
Assignment about What is Probability?_2

Probability 3
Pr(𝐶/𝐴) = Pr(𝐶) Pr(𝐶 ∩ 𝐴)
Pr(𝐴)
=
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
Assignment about What is Probability?_3

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