# Ashworth Probabilities in Families with 4 Children Statistical Analysis

Anonymous

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proggerardo
School: Duke University

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1. Probabilities in families with four children.
Number of girl children in the family
1
2
3
BBBG
BBGG
BGGG
BBGB
BGBG
GGGB
BGBB
BGGB
GGBG
GBBB
GGBB
GBGG
GBGB
GBBG

0
BBBB

a) 𝑃(1) =
b) 𝑃(2) =
c) 𝑃(4) =

𝑛𝑢𝑚𝑏𝑒𝑟 𝑒𝑣𝑒𝑛𝑡𝑠 𝑓𝑜𝑟 1 𝑔𝑖𝑟𝑙
𝑛𝑢𝑚𝑏𝑒𝑟 𝑡𝑜𝑡𝑎𝑙 𝑒𝑣𝑒𝑛𝑡𝑠

𝑛𝑢𝑚𝑏𝑒𝑟 𝑒𝑣𝑒𝑛𝑡𝑠 𝑓𝑜𝑟 2 𝑔𝑖𝑟𝑙𝑠
𝑛𝑢𝑚𝑏𝑒𝑟 𝑡𝑜𝑡𝑎𝑙 𝑒𝑣𝑒𝑛𝑡𝑠
𝑛𝑢𝑚𝑏𝑒𝑟 𝑒𝑣𝑒𝑛𝑡𝑠 𝑓𝑜𝑟 4 𝑔𝑖𝑟𝑙𝑠

d) 𝑃(3𝑟𝑑 ) =

𝑛𝑢𝑚𝑏𝑒𝑟 𝑡𝑜𝑡𝑎𝑙 𝑒𝑣𝑒𝑛𝑡𝑠

4

1

= 16 = 4 = 0.25
6

3

= 16 = 8 = 0.375
1

= 16 = 0.062

𝑛𝑢𝑚𝑏𝑒𝑟 𝑒𝑣𝑒𝑛𝑡𝑠 𝑓𝑜𝑟 𝑎 𝑔𝑖𝑟𝑙 𝑖𝑛 𝑡ℎ𝑖𝑟𝑑 𝑐ℎ𝑖𝑙𝑑
𝑛𝑢𝑚𝑏𝑒𝑟 𝑡𝑜𝑡𝑎𝑙 𝑒𝑣𝑒𝑛𝑡𝑠

8

1

= 16 = 2 = 0.5

2. Roulette wheel probabilities
a) Green numbers (0, 00).
𝑛𝑢𝑚𝑏𝑒𝑟 𝑒𝑣𝑒𝑛𝑡𝑠 𝑓𝑜𝑟 𝑔𝑟𝑒𝑒𝑛
2
1
𝑃(𝐺) =
=
=
= 0.0526
𝑛𝑢𝑚𝑏𝑒𝑟 𝑡𝑜𝑡𝑎𝑙 𝑒𝑣𝑒𝑛𝑡𝑠
38 19
b) Number greater than 30 (31, 32, 33, 34, 35, 36)
𝑛𝑢𝑚𝑏𝑒𝑟 𝑒𝑣𝑒𝑛𝑡𝑠 𝑓𝑜𝑟 𝑣 > 30
6
3
𝑃(𝑣 > 30) =
=
=
= 0.1579
𝑛𝑢𝑚𝑏𝑒𝑟 𝑡𝑜𝑡𝑎𝑙 𝑒𝑣𝑒𝑛𝑡𝑠
38 19
c) Red number less than 10 (8, 6, 4, 2)
𝑛𝑢𝑚𝑏𝑒𝑟 𝑒𝑣𝑒𝑛𝑡𝑠 𝑓𝑜𝑟 𝑅 < 10
4
2
𝑃(𝑅 < 10) =
=
=
= 0.1053
𝑛𝑢𝑚𝑏𝑒𝑟 𝑡𝑜𝑡𝑎𝑙 𝑒𝑣𝑒𝑛𝑡𝑠
38 19
d) Even black number (none, black numbers are odd)
𝑛𝑢𝑚𝑏𝑒𝑟 𝑒𝑣𝑒𝑛𝑡𝑠 𝑓𝑜𝑟 𝐵 = 𝑒𝑣𝑒𝑛
0
𝑃(𝐵 = 𝑒𝑣𝑒𝑛) =
=
=0
𝑛𝑢𝑚𝑏𝑒𝑟 𝑡𝑜𝑡𝑎𝑙 𝑒𝑣𝑒𝑛𝑡𝑠
38
e) Expected green in 57,000 spins.
2
𝐸 = 𝑁 × 𝑃(𝐺) = 57,000 ×
= 3,000
38

4
GGGG

3. Pizza Poll
a) By the inspection of the percentages of pizza acceptance in US residents from two polls
with one month of difference, it is not possible to conclude that there is a decline in
pizza popularity. It is important to consider th...

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