Answer :
Hello,
Choice urn_1: 1/3
choice R: 5/8 ==>1/3*5/8=5/24
Choice urn_2: 1/3
Choice R: 3/4 ==> 1/3*3/4=1/4
Choice urn_3: 1/3
Choice R:4/6=2/3 ==> 1/3*2/3=2/9
Total: 5/24+1/4+2/9=15/72+18/72+16/72=49/72
Choice urn_1: 1/3
choice R: 5/8 ==>1/3*5/8=5/24
Choice urn_2: 1/3
Choice R: 3/4 ==> 1/3*3/4=1/4
Choice urn_3: 1/3
Choice R:4/6=2/3 ==> 1/3*2/3=2/9
Total: 5/24+1/4+2/9=15/72+18/72+16/72=49/72
Answer:
The probability of getting red balls is 0.68.
Step-by-step explanation:
Given : Urn 1 contains 5 red balls and 3 black balls. Urn 2 contains 3 red balls and 1 black ball. Urn 3 contains 4 red balls and 2 black balls. If an urn is selected at random and a ball is drawn.
To find : The probability it will be red ?
Solution :
Total urn = 3
If an urn is selected at random then the probability is [tex]P(U)=\frac{1}{3}[/tex]
In urn 1 - 5 red balls + 3 black balls
Probability of getting red ball from urn 1 - [tex]P(R_1)=\frac{5}{8}[/tex]
In urn 2 - 3 red balls + 1 black balls
Probability of getting red ball from urn 2 - [tex]P(R_2)=\frac{3}{4}[/tex]
In urn 3 - 4 red balls + 2 black balls
Probability of getting red ball from urn 3 - [tex]P(R_3)=\frac{4}{6}[/tex]
Choosing red ball from urn is [tex]P(R)=P(R_1)+P(R_2)+P(R_3)[/tex]
[tex]P(R)=\frac{5}{8}+\frac{3}{4}+\frac{4}{6}[/tex]
[tex]P(R)=\frac{15+18+16}{24}[/tex]
[tex]P(R)=\frac{49}{24}[/tex]
The probability of getting red balls is
[tex]P=P(U)\times P(R)[/tex]
[tex]P=\frac{1}{3}\times \frac{49}{24}[/tex]
[tex]P=\frac{49}{72}[/tex]
[tex]P=0.68[/tex]