By signing in you confirm you are 18 or older, or have your parent’s or guardian’s consent.

NDA 1 2024 Maths, question 109

Topic: Probability

Q109

Let m=77nm=77^{n}. The index nn is given a positive integral value at random. What is the probability that the value of mm will have 11 in the units place ?

  1. (a) 12\frac{1}{2}
  2. (b) 13\frac{1}{3}
  3. (c) 14\frac{1}{4}Correct answer
  4. (d) 1n\frac{1}{n}

Solution.

Answer: (c) 14\frac{1}{4}

  1. The last digit of 77n77^{n} follows that of 7n7^{n}: 7, 9, 3, 1, then repeats every 4.
  2. It is 1 exactly when nn is a multiple of 4, one case in every four.
  3. So the probability is 14\frac{1}{4}.

Trap: A random positive integer has no exact equal-chance rule; the answer takes the four positions in the cycle as equally likely.