A survey in 2020 asked 100 people in 3 rounds if they thought women in the police forces should be permitted to participate in combat. The results of the survey are shown.

1. A survey in 2020 asked 100 people in 3 rounds if they thought women in the police
forces should be permitted to participate in combat. The results of the survey are
shown.
Gender Yes No Total
Male 32 18 50
Female 8 42 50
Total 40 60 100
Find the following probabilities.
a) The respondentanswered yes, given that the respondent was a female.
b) The respondent was a male, given that the respondent answered no.
Solution
Let M = Male
F = Female
Y = Yes
N = No
(a)𝑷(𝒀
𝑭
⁄ ) =
𝑷(𝒀∩𝑭)
𝑷(𝑭)
=
𝑷(𝒀∩𝑭)
𝑷(𝒀∩𝑭)+𝑷(𝑵∩𝑭)
=
𝟖
𝟏𝟎𝟎
⁄
𝟖
𝟏𝟎𝟎
⁄ +𝟒𝟐
𝟏𝟎𝟎
⁄
=
𝟖
𝟓𝟎
= 𝟎. 𝟏𝟔
(b)𝑷(𝑴
𝑵
⁄ ) =
𝑷(𝑴∩𝑵)
𝑷(𝑵)
=
𝑷(𝑴∩𝑵)
𝑷(𝑴∩𝑵)+𝑷(𝑭∩𝑵)
=
𝟏𝟖
𝟏𝟎𝟎
⁄
𝟏𝟖
𝟏𝟎𝟎
⁄ +𝟒𝟐
𝟏𝟎𝟎
⁄
=
𝟏𝟖
𝟔𝟎
= 𝟎. 𝟑