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At a small college, 90% of nursing majors have volunteer experience at a hospital and 80% of nursing majors have a GPA of 3.7 or better. If one nursing major is selected at random, and volunteer experience is independent of GPA, what is the probability that the student has no volunteer experience and has a GPA of 3.7 or better?

Respuesta :

MrRoyal

Answer:

[tex]P(V'\ or\ GP) = 90\%[/tex]

Step-by-step explanation:

Represent

Volunteer Experience with V

GPA of 3.7 or better with GP

No Volunteer Experience with V'

Given

[tex]P(V) = 90\%[/tex]

[tex]P(GP) = 80\%[/tex]

Required

Determine the probability that the student has no volunteer experience and has a GPA of 3.7 or better

The required probability can be represented using:

[tex]P(V'\ or\ GP)[/tex]

And this is calculated as thus:

[tex]P(V'\ or\ GP) = P(V') + P(GP)[/tex]

Where

[tex]P(V') = 1 - P(V)[/tex] -------------- Complements of Probability

So:

[tex]P(V'\ or\ GP) = P(V') + P(GP)[/tex]

[tex]P(V'\ or\ GP) = 1 - P(V) + P(GP)[/tex]

[tex]P(V'\ or\ GP) = 1 - 90\% + 80\%[/tex]

[tex]P(V'\ or\ GP) = 90\%[/tex]

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