Respuesta :
Answer:[tex]\frac{8}{11}[/tex]
Step-by-step explanation:
Given
Probability of selecting Paper bag is equivalent to getting a head in coin i.e. 0.5 and probability of selecting Plastic bag is equivalent to getting a tail in coin i.e. 0.5
Probability of getting a red ball from Paper bag[tex]=\frac{2}{3}[/tex]
Probability of getting a red ball from Plastic bag[tex]=\frac{1}{4}[/tex]
If a red ball is selected Probability that it came from the paper bag
[tex]P=P(Red\ ball\ from\ paper\ bag|Red\ ball)[/tex]
[tex]P=\frac{\frac{1}{2}\times \frac{2}{3}}{\frac{1}{2}\times \frac{2}{3}+\frac{1}{2}\times \frac{1}{4}}[/tex]
[tex]P=\frac{2}{2+\frac{3}{4}}=\frac{8}{11}[/tex]
If a red ball is selected, the probability that it came from the paper bag is; ⁸/₁₁
How to use Baye's theorem for conditional Probability?
When tossing a coin, the probability of getting a head is equal to the probability of getting a tail which is 0.5.
Now, since the probability of selecting paper bag is equal to getting a head and probability of selecting Plastic bag is equal to getting a tail, then;
Probability of getting a red ball from Paper bag = 2/3
Probability of getting a red ball from Plastic bag = 1/4
Thus, using Baye's theorem, If a red ball is selected, the probability that it came from the paper bag is;
P(Red ball from paper bag|Red ball) = (¹/₂ * ²/₃)/((¹/₂ * ²/₃) + (¹/₂ * ¹/₄))
P(Red ball from paper bag|Red ball) = ⁸/₁₁
Read more about Baye's theorem at; https://brainly.com/question/16038936
