From a basket with 6 white hats and 3 black hats, one is chosen at random. If the hat is white, a handkerchief is taken at random from a drawer that contains 2 white, 2 black and 5 with white and black checks. If the hat is black, a handkerchief is chosen at random from another drawer that contains 2 white handkerchiefs, 4 black and 4 with white and black checks. It is requested: a) (1 point) Calculate the probability that the handkerchief shows some color that is not the color of the hat. b) (0.5 points) Calculate the probability that in at least one of the accessories (hat or handkerchief) the color black appears. c) (1 point) Calculate the probability that the hat was black, knowing that the handkerchief was checked.
From a basket with 6 white hats and 3 black hats, one is chosen at random. If the hat is white, a handkerchief is taken at random from a drawer that contains 2 white, 2 black and 5 with white and black checks. If the hat is black, a handkerchief is chosen at random from another drawer that contains 2 white handkerchiefs, 4 black and 4 with white and black checks. It is requested:\\
a) (1 point) Calculate the probability that the handkerchief shows some color that is not the color of the hat.\\
b) (0.5 points) Calculate the probability that in at least one of the accessories (hat or handkerchief) the color black appears.\\
c) (1 point) Calculate the probability that the hat was black, knowing that the handkerchief was checked.