P(B/A) is  in the simplest form
 in the simplest form
Step-by-step explanation:
Let us explain how to solve the problem
- P(B|A) is called the "Conditional Probability" of B given A
- Conditional probability is the probability of one event occurring with some relationship to one or more other events that means event A has already happened, now what is the chance of event B
- The formula for conditional probability is P(B|A) = P(A and B)/P(A), where P(A and B) is P(A) . P(B given A occurred)
∵ There are 3 red marbles, 5 green marbles, and 2 blue 
    marbles in the jar
∴ The total number of the marbles in the jar = 3 + 5 + 2 = 10
∵ Two marbles are drawn from the bag, one after the other without
    replacement
- That means red is already occurred when green is happened,
   so it is a "Conditional Probability" of green given red 
   P(B/A) = P(A and B)/P(A)
∵ Event A is defined as drawing a red marble from the jar on
    the first draw
∴ P(A) = P(red)
∵ P(red) = 
∴ P(A) = 
∵ Event B is defined as drawing a green marble on the second draw
∴ P(B) = P(green)
- The number of marbles after the red is chosen is 9 
∵ P(green) = 
∴ P(B) = 
- Find P( A and B)
∴ P(A and B) = (  ) . (
 ) . (  )
 )
∴ P(A and B) = 
- Simplify the fraction by divide up and down by 15
∴ P(A and B) = 
∵ P(B|A) = P(A and B)/P(A)
- Substitute the values of P(A and B) and P(A) in the rule above
∴ P(B/A) = 
- Simplify the fraction
∵  ÷
 ÷  =
 =  ×
 ×  =
 = 
- Divide up and down by 2
∴ P(B/A) = 
P(B/A) is  in the simplest form
 in the simplest form
Learn more: 
You can learn more about probability in brainly.com/question/10744457
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