Kevin hosts the TV programme Thank Your Lucky Stars. During the show he picks members of the large studio audience at random and asks them what
star sign they were born under.
(There are 12 star signs in all and you may assume that the probabilities that
a randomly chosen person will be born under each star sign are equal.)
(i) The first person Kevin picks says that he was born under the star sign
Aries. What is the probability that the next person he picks was not born
under Aries?
(ii) Show that the probability that the first three people picked were all born
under different star signs is approximately 0.764.
(iii) Calculate the probability that the first five people picked were all born
under different star signs.
(iv) What is the probability that at least two of the first five people picked
were born under the same star sign?