Answer: a. 0.40 b. 0.23 c . 0.435 d . 0.25
Step-by-step explanation:
melanin content Total
high low
moisture high 13 10 23
content low 47 30 77
Total 60 40 100
Let A denote the event that a sample has low melanin content, and let B denote the event that a sample has high moisture content.
a) Total skin samples has low melanin content = 10+30=40
P(A)=[tex]\dfrac{40}{100}=0.40[/tex]
b) Total skin samples has high moisture content = 13+10=23
P(B) =[tex]\dfrac{23}{100}=0.23[/tex]
c) A ∩ B = Total skin samples has both low melanin content and high moisture content =10
P(A ∩ B) =[tex]\dfrac{10}{100}=0.10[/tex]
Using conditional probability formula , [tex]P (A|B)=\dfrac{P(A\cap B)}{P(B)}[/tex]
[tex]P (A|B)=\dfrac{0.10}{0.23}=0.434782608696\approx0.435[/tex]
d) [tex]P (B|A)=\dfrac{P(A\cap B)}{P(A)}[/tex]
[tex]P (B|A)=\dfrac{0.10}{0.40}=0.25[/tex]
