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Find the probability that either event a or b occurs if the chance of a occurring is .5, the chance of b occurring is .3, and events a and b are independent.

Respuesta :

Using Venn probabilities and independent events, it is found that the probability that either event a or b occurs is of 0.65 = 65%.

What is a Venn probability?

In a Venn probability, two events are related with each other, as are their probabilities.

The "or probability" is given by:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

What are independent events?

If two events, A and B, are independent, we have that:

[tex]P(A \cap B) = P(A)P(B)[/tex]

In this problem, the probabilities are:

  • [tex]P(A) = 0.5, P(B) = 0.3[/tex].
  • Since they are independent, [tex]P(A \cap B) = P(A)P(B) = 0.5(0.3) = 0.15[/tex]

Hence:

[tex]P(A \cup B) = 0.3 + 0.5 - 0.15 = 0.65[/tex]

The probability that either event a or b occurs is of 0.65 = 65%.

You can learn more about  Venn probabilities and independent events at https://brainly.com/question/14478923

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