Answer:
The probability that the market will be actaully favourable is 0.9084
Explanation:
Lets put names to the events
F = The market is favourable
U = The market is favourable (this is F^c)
PF = Gazelle predicts that the market is favourable
PU = Gazelle predicts that the market is unfavourable (this is PF^c)
Also, we know that
P(F) = 0.7
P(U) = 0.3
P(PF | F) = 0.85
P(PU | F) = 0.15
P(PF | U) = 0.2
P(PU | U) = 0.8
We want to know P(F |PF), we can obtain this probability using the ones that we are given and the Bayes Formula

The probability that the market will be actaully favourable is 0.9084