An urn contains different colored marbles. The probability of drawing two green marbles from the urn without replacement is 3/20 , and the probability of drawing one green marble is 2/5 . What is the probability of drawing a second green marble, given that the first marble is green?3/501/23/81/5
Accepted Solution
A:
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]