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A local school has 14 kindergarten teachers. Of these teachers, 4 are Hispanic, 5 are bilingual, and 3 are both Hispanic and bilingual. If a kindergarten teacher is selected at random, what is the probability that teacher is Hispanic or bilingual? P(Hispanic or Bilingual) = Give answer as decimal (not percent) and round to 3 decimal places.

Respuesta :

Answer:

P(Hispanic or Bilingual) = 0.429.

Step-by-step explanation:

This question is solved treating these events as Venn probabilities.

I am going to say that:

Event A: Hispanic

Event B: Bilingual

Out of 14 teachers, 4 are Hispanic, 5 are billingual, and 3 are both:

This means that:

[tex]P(A) = \frac{4}{14}, P(B) = \frac{5}{14}, P(A \cap B) = \frac{3}{14}[/tex]

What is the probability that teacher is Hispanic or bilingual?

This is:

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

With the values that the exercise gives us:

[tex]P(A \cup B) = \frac{4}{14} + \frac{5}{14} - \frac{3}{14} = \frac{4 + 5 - 3}{14} = \frac{6}{14} = 0.429[/tex]

So

P(Hispanic or Bilingual) = 0.429.

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