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JEE Advanced 2015Paper 1
Exam
JEE Advanced
Year
2015
Paper
Paper 1
Subject
Mathematics
Chapter
Probability

JEE Advanced 2015 · Paper 1 · Mathematics · Probability

The minimum number of times a fair coin needs to be tossed so that...

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 0.960 . 96, is

Correct answer

8

Step-by-step solution

P(2)+P(3)…≥0.96P\left(2\right) + P\left(3\right) \ldots \ge 0 .96
1−P(0)−P(1)≥0.961 - P\left(0\right) - P\left(1\right) \ge 0 .96
1−0.96≥nC0(12)n+nC1(12)n1 - 0 .96 {\ge}^{n}{C}_{0}{\left(\dfrac{1}{2}\right)}^{n}{+}^{n}{C}_{1}{\left(\dfrac{1}{2}\right)}^{n}
⇒(0.04)2n≥1+n⇒ \left(0 .04\right){2}^{n} \ge 1 + n
⇒4.2n≥(n+1)100⇒ 4{.2}^{n} \ge \left(n + 1\right)100
⇒2n+2≥(n+1)100⇒ {2}^{n + 2} \ge \left(n + 1\right)100
As, 210≥900{2}^{10} \ge 900
⇒n=8⇒ n = 8
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