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NDA 1 2024 Maths, question 116

Topic: Probability

Passage · Q115 to Q116

An unbiased coin is tossed nn times. The probability of getting at least one tail is pp and the probability of at least two tails is qq and p−q=532p-q=\frac{5}{32}.

Q116

What is the value of p+qp+q ?

  1. (a) 5732\frac{57}{32}Correct answer
  2. (b) 5332\frac{53}{32}
  3. (c) 5132\frac{51}{32}
  4. (d) 11

Solution.

Answer: (a) 5732\frac{57}{32}

  1. With n = 5, p = 1 − 1/32 = 31/32.
  2. Exactly one tail has probability 5/32, so q = 26/32.
  3. Therefore p + q = 57/32.