Let F, L, and V denote the events that a customer avails loan at fixed rate, floating rate, and variable rate, respectively. Let D denote the event that a customer defaults on loan repayment.

We are given:

• P(F) = 0.10
• P(L) = 0.20
• P(V) = 0.70
• P(D|F) = 0.05
• P(D|L) = 0.03
• P(D|V) = 0.01

We want to find P(V|D), the probability that the customer availed the loan at a variable rate given that they defaulted.

Using Bayes' Theorem:

P(V|D) = [P(D|V) * P(V)] / P(D)

First, we need to find P(D), the probability of default. We can use the law of total probability:

P(D) = P(D|F) * P(F) + P(D|L) * P(L) + P(D|V) * P(V)

P(D) = (0.05 * 0.10) + (0.03 * 0.20) + (0.01 * 0.70)

P(D) = 0.005 + 0.006 + 0.007

P(D) = 0.018

Now we can find P(V|D):

P(V|D) = (0.01 * 0.70) / 0.018

P(V|D) = 0.007 / 0.018

P(V|D) = 7/18