probabbility question

Question

A public-interest group was planning to file a case in consumer court to challenge the of charging "surge pricing" by urban ride hailing companies in one of three cities. New Delhi, Mumbai, or Kolkata. The probability that it would choose New Delhi was 0.40; Mumbai, 0.35; and Kolkata, 0.25. The group also knew that it had a 60 percent chance of a favourable ruling if it chose Mumbai, 45 percent if it chose New Delhi, and 35 percent if i chose Kolkata. If the group did receive a favourable ruling, which city did it most likely choose?

Answer 1

The probability of choosing New Delhi is 0.4, but only 0.45 of this would be a favourable choice=0.4×0.45=0.18, the combined probability.

Similarly, for Mumbai this overall probability would be 0.35×0.6=0.21; and for Kolkata 0.25×0.35=0.0875.

The largest combined probability goes to Mumbai, the most likely choice.