Question

2 and only 2 independent factors influence my happiness: My salary and the weather.
The probability that I have a high salary is 0.2
The probability that it is sunny is 0.95

The probability that I am happy, given that I have a high salary and it is sunny is 0.99
The probability that I am happy given that it is gloomy and I have a high salary is 0.8
The probability that I am happy given it is sunny and that I have a low salary is 0.6
The probability that I am happy given the weather is gloomy and I have a low salary is 0.1

Find the probability that I have a high salary, given that it is sunny

Answer 1

look ai-class video :D

Answer 2

You said that the two events, your salary and the weather are independent (i.e the occurrence of one even does NOT affect the probability of the other),
\[P(\text{ high salary}|\text{sunny})=P(\text{ high salary})=0.2 \text{ .}\]

Answer 3

event*