Respuesta :

mhanifa

17/35

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To find the probability that only one of two people will win a race, given their individual probabilities, we need to use the following logic:

  • Person A wins, and Person B does not win.
  • Person B wins, and Person A does not win.

The probability of Person A winning is 2/5, and thus the probability of Person A not winning is 1 - 2/5 = 3/5.

Similarly, the probability of Person B winning is 3/7, and the probability of Person B not winning is 1 - 3/7 = 4/7.

We calculate the probability of each scenario separately:

  • Person A wins, Person B does not ⇒  (2/5) * (4/7)
  • Person B wins, Person A does not ⇒  (3/7) * (3/5)

Now, we add the probabilities of these two mutually exclusive events to find the overall probability that only one will win:

  • ((2/5) * (4/7)) + ((3/7) * (3/5)) = (8/35) + (9/35) = 17/35

Therefore, the probability that only one of them will win the race is 17/35.

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