8 2 3 2 3 1 2 Dice A Dice B The diagram shows two fair dice. Dice A is numbered 1, 2, 2, 2, 3, 6. Dice B is numbered 2, 3, 3, 4, 4, 4. (a) (i) Dice A is rolled once. Write down the probability that it lands on the number 6. ................................................. [1] (ii) Dice A is rolled 150 times. Find the number of times it is expected to land on the number 6. ................................................. [1] (b) Dice A and Dice B are each rolled once. (i) Find the probability that the two numbers they land on have a total of 6. ................................................. [3] (ii) Find the probability that when the two numbers they land on have a total of 6, both numbers are 3. ................................................. [2] © UCLES 2023 0580/42/O/N/23 13 (c) Dice B is rolled n times. 32 The probability that on the nth roll it first lands on a number 3 is . 729 Find the value of n. n = ................................................ [2] © UCLES 2023 0580/42/O/N/23 [Turn over 14