Respuesta :
Answer:
No the solution is incorrect.
p(black piece of clothing or a shirt) = [tex]\frac{17}{24}[/tex]
Step-by-step explanation:
given
No. of black shirts = 3
No. of blue shirts = 8
No. of black pants = 6
No. of blue pants = 7
Total no. of clothing = 24
No. of black piece of clothing = 3+6 = 9
No. of shirts = 3+8 = 11
Problem is : Probability p(black piece of clothing or a shirt)
In In probability 'or' means that the outcome must satisfy one condition or other condition or both. We have to apply addition rule: when two events A and be are mutually exclusive, the probability that A or B will occur is given by
P(A U B) = P(A) +P(B)
Also when two events A and be are non-mutually exclusive, the probability that A or B will occur is given by
P(A U B) = P(A) +P(B) - P(A ∩ B)
The given problem falls under non-mutually exclusive
Hence
p(black piece of clothing or a shirt) = p(black piece of clothing) +p(a shirt) - p(black piece of clothing and a shirt)
[Here p(black piece of clothing and a shirt) is no of black shirts/total no of clothing]
p(black piece of clothing or a shirt) = [tex]\frac{9}{24}[/tex] + [tex]\frac{11}{24}[/tex] - [tex]\frac{3}{24}[/tex]
= [tex]\frac{17}{24}[/tex]
Hence p(black piece of clothing or a shirt) = [tex]\frac{17}{24}[/tex]
