Respuesta :
Answer:
The probability of drawing a second green marble, given that the first marble is green is:
[tex]\dfrac{3}{8}[/tex]
Step-by-step explanation:
Let A denote the event that first marble is green.
B denote the event that the second marble is green.
A∩B denote the event that both the marbles are green.
Let P denote the probability of an event.
We are asked to find:
P(B|A) i.e. probability of drawing a second green marble, given that the first marble is green.
We know that:
[tex]P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}[/tex]
Probability of drawing one green marble is 2/5 i.e.
[tex]P(A)=\dfrac{2}{5}[/tex]
The probability of drawing two green marbles from the urn without replacement is 3/20 i.e.
[tex]P(A\bigcap B)=\dfrac{3}{20}[/tex]
Hence, we have:
[tex]P(B|A)=\dfrac{\dfrac{3}{20}}{\dfrac{2}{5}}\\\\\\i.e.\\\\\\P(B|A)=\dfrac{3\times 5}{20\times 2}\\\\\\P(B|A)=\dfrac{3}{8}[/tex]
