I have this exercise that confuses me a lot and i do not know what method to use.
Any ideas ?
The philosophy professor has three berets and a cap. On Saturday he stays at home in slippers and only goes down to buy bread. When he leaves he chooses a hat at random. Knowing that he buys a baguette once in three and that once in five forgets to put on his shoes, calculate the probability that he returns in slippers, with the beret on his head and the baguette under his arm.
What i understood is that:
P(Beret) = 3/4 = 0.75
P(cap) = 1/4 = 0.25
P(Baguette) = 1/3 = 0.33
How do i proceed, is it a conditional probability ?
Or is it P(HasShoes)*(P(beret) and P(baguette))
$ 0.80*(0.75*0.33)=0.198 = 19.8 % $ ?