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The ratio 9:7 gives you following statement:

  • Carl will win in 9 cases from 9+7=16;
  • Carl will lose in 7 cases from 16.

Then the probability that Carl will lose is

[tex]Pr(\text{Carl will lose})=\dfrac{7}{16}.[/tex]

Answer: [tex]Pr(\text{Carl will lose})=\dfrac{7}{16}.[/tex]