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← JEE Advanced 2015 · Paper 1
MathematicsInteger+4Question 43 of 60

JEE Advanced 2015 · Paper 1, Mathematics question 43

The minimum number of times a fair coin needs to be tossed, so that the probability of getting at least two heads is at least 0.96, is

Answer and worked solution

Official answer: 8

Probability. P(at least two heads in nn tosses) =1−1+n2n=1-\dfrac{1+n}{2^n}. We need
n+12n≤0.04.\frac{n+1}{2^n}\le0.04.

Check values.

  • n=7n=7: 8128=0.0625\frac8{128}=0.0625, too large.
  • n=8n=8: 9256≈0.035\frac9{256}\approx0.035. ✓

Answer: 8