When a person needs a minicab, it is hired from one of three firms, X, Y and Z. Of the hirings 40% are from X, 50% are from Y and 10% are from Z. For cabs hired from X, 9% arrive late, the corresponding percentages for cabs hired from firms Y and Z being 6% and 20% respectively. Calculate the probability that the next cab hired

(a) will be from X and will not arrive late,

(b) will arrive late. Given that a call is made for a minicab and that it arrives late, find, to three decimal places, the probability that it came from Y. (L)