Answer:
The probability is  [tex]P(K)  =  \frac{ 28 }{195} [/tex]
Step-by-step explanation:
From the question we are told that
  The number of green marbles is  [tex]n_g  =  3[/tex]
  The number of red marbles is  [tex]n_b  =  5[/tex]
   The number of red marbles is  [tex]n_r  =  7[/tex]
Generally the total number of marbles is mathematically represented as
    [tex]n_t  =  n_r  +  n_g + n_ b[/tex]
    [tex]n_t  =  7 +  3 + 5[/tex]
     [tex]n_t  = 5 [/tex]
Generally total number of marbles that are not red is Â
   [tex]n_k  =  n_g +  n_ b[/tex]
=>  [tex]n_k  =  3 +  5[/tex]
=>  [tex]n_k  =  8[/tex]
The probability of the first ball not being red is mathematically represented as Â
   [tex]P(r') =  \frac{n_k}{n_t}[/tex]
=> Â [tex]P(r') = Â \frac{ 8}{15}[/tex]
The probability of the second ball not being red is mathematically represented as
   [tex]P(r'') =  \frac{n_k - 1}{n_t -1}[/tex]
=>  [tex]P(r'') =  \frac{ 8 -1 }{15-1}[/tex] (the subtraction is because the marbles where selected without replacement  )
=> Â [tex]P(r'') = Â \frac{ 7 }{14}[/tex]
The probability that the first two balls  is  not red is mathematically represented as
  [tex]P(R) =  P(r') *  P(r'')[/tex]
=> Â [tex]P(R) = Â \frac{ 8}{15} * Â \frac{ 7 }{14}[/tex]
=> Â [tex]P(R) = Â \frac{ 8 }{30}[/tex]
The probability of the third ball being red is mathematically represented as
  [tex]P(r) =  \frac{n_r}{ n_t -2}[/tex] (the subtraction is because the marbles where selected without replacement  )
   [tex]P(r) =  \frac{7}{ 15 -2}[/tex]
=> Â Â [tex]P(r) = Â \frac{7}{ 13}[/tex]
Generally the probability of the first two marble not being red and the third marble being red is mathematically represented as
    [tex]P(K)  =  P(R) * P(r)[/tex]
     [tex]P(K)  =  \frac{ 8 }{30} * \frac{7}{ 13}[/tex]
=> Â Â Â [tex]P(K) Â = Â \frac{ 28 }{195} [/tex]
