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JEE Main 2019 · 10 April · Shift II

JEE Main 2019 Mathematics question on Probability

Minimum number of times a fair coin must be tossed so that the probability of getting atleast one head is more than 99% is
  1. A.
    8
  2. B.
    6
  3. C.
    7
  4. D.
    5
Show answer and solution

Correct option: C

Solution

We need P(at least one head) > 0.99, which means 1 - P(no heads) > 0.99, so P(all tails) < 0.01.

P(all tails in n tosses) = (1/2)n < 1/100.

(1/2)6 = 1/64 ≈ 0.0156 > 0.01 → not sufficient.
(1/2)7 = 1/128 ≈ 0.0078 < 0.01 → sufficient.

So minimum n = 7.

[JEE Main 2019 · 10 April · Shift II]

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