A scone contains raisins and sultanas. Prove that inside the scone there will always be two points 1cm apart such that either both lie inside raisins, both inside sultanas, or both lie outside of either raisins or sultanas.
40% of adherents of some political party are women. 70% of the adherents of this party are townspeople. At the same time, 60% of the townspeople who support the party are men. Are the events “the adherent of the party is a townsperson” and “the adherent of party is a woman” independent?