A-LevelMathematicsProbability and statistics9709/51 · May/June 2025 · Q27 Marks
Find the number of different arrangements of the 8 letters in the word KANGAROO in which the two As are together and the two Os are not together.
- (a)Find the number of different arrangements of the 8 letters in the word KANGAROO in which the two As are together and the two Os are not together.[3]
- (b)A fair 8-sided dice has faces labelled K, A, N, G, A, R, O, O. The dice is rolled repeatedly. Find the probability that fewer than 6 rolls of this dice are required to obtain an A.[2]
- (c)Find the probability that the second A is obtained on the 6th roll of the dice.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.
- [M1] Method 1: 7!/2 - k, where k is an integer ≥ 1. Method 2: 5! x p, where p is an integer > 1.
- [M1] Method 1: n - 6!, where n is an integer > 720. Method 2: q x 6x5/2, q x 6C2, q x 6P2, q x 6 x 5, q an integer > 1.
- [A1] 1800
- [M1] Method 1: 1 - (3/4)^a, a = 5, 6. Method 2: 1/4 + (1/4)(3/4) + (1/4)(3/4)^2 + (1/4)(3/4)^3 + (1/4)(3/4)^4.
- [A1] 0.7626 < p < 0.763.
- [M1] p^2 (1-p)^x * 5, 0 < p < 1, p ≠ 1-p.
- [A1] AWRT
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