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The nursing department of a college surveyed two hundred graduates from their programs about their current
work. The college has different levels of degrees in nursing available. The department found the following
probabilities:
P(bachelor's degree) = 0.45
P(working in nursing) = 0.85
Pin nursing and bachelor's) = 0.4
Find the probability that a graduate is currently working in nursing, given that they earned a bachelor's degree.

Respuesta :

Answer: The required probability is 0.008.

Step-by-step explanation:

Since we have given that

Probability of bachelor's degree = 0.45

Probability of working in nursing = 0.85

Probability of both = 0.4

So, Probability of getting a graduate is currently working in nursing, given that they earned a bachelor's degree would be :

[tex]P(N|B)=\dfrac{P(N\cap B)}{P(B)}\\\\P(N|B)=\dfrac{0.4}{0.45}\\\\P(N|B)=0.008[/tex]

Hence, the required probability is 0.008.

Using conditional probability, it is found that there is a 0.8889 = 88.89% probability that a graduate is currently working in nursing, given that they earned a bachelor's degree.

Conditional Probability

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

  • P(B|A) is the probability of event B happening, given that A happened.
  • [tex]P(A \cap B)[/tex] is the probability of both A and B happening.
  • P(A) is the probability of A happening.

In this question:

  • Event A: Bachelor's degree.
  • Event B: Working in nurse.

From the probabilities given, we have that [tex]P(A \cap B) = 0.4, P(A) = 0.45[/tex]

Hence:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4}{0.45} = 0.8889[/tex]

0.8889 = 88.89% probability that a graduate is currently working in nursing, given that they earned a bachelor's degree.

A similar problem is given at https://brainly.com/question/14398287

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