If a credit application is selected at random, what is theprobability that it is

Question

If a credit application is selected at random, what is theprobability that it is approved?

What is the probability that an application containing `gender = a'is approved

If an application with `gender = b' is selected at random, what isthe probability that is has been approved?

Using you answers from the above or otherwise, are columns(Gender) and ( X ) statistically dependent or independent?

Gender   X (Approved/ Not Approved) a   approved a approved a not approved a approved b approved b not approved b not approved

Explanation / Answer

n(Gender a) = 4
n(Gender b) = 3 n(approved) = 4 n(not approved) = 3 1) P(approved) = 4/7 = 0.5714 2) P(approved/Gendera) = n(approved & Gender a) / n(Gendera) = 3/4 = 0.75 (conditional probability) 3) P(approved/Gender b) = n(approved & Gender b)/n(Genderb) = 1/3 = 0.3333 (conditional probability) Hope this helps.

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