4 (a) Lucia has two fair spinners. Spinner A is five-sided and is numbered 1, 2, 3, 4, 5. Spinner B is nine-sided and is numbered 3, 3, 3, 4, 4, 4, 4, 5, 5. Lucia spins the two spinners and records whether they land on a prime number. (i) Complete the tree diagram. Spinner A Spinner B prime ............ prime 3 5 not ............ prime prime ............ not ............ prime not ............ prime [2] (ii) Find the probability that (a) the two numbers are both prime ................................................. [2] (b) the two numbers are not both prime. ................................................. [1] © UCLES 2023 0580/41/O/N/23 7 (b) Lucia spins Spinner A 120 times. Find the expected number of times the spinner lands on a prime number. ................................................. [1] (c) Lucia spins Spinner B twice. Find the probability that the two numbers it lands on add up to 9 or more. ................................................. [3] (d) Lucia keeps spinning Spinner B until it lands on a 4. Find an expression, in terms of n, for the probability that this happens on the nth spin. ................................................. [2] © UCLES 2023 0580/41/O/N/23 [Turn over 8