JEE Main · 2019 · 08 Apr 2019 · Shift 2 · Probability

The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at least

90%

is:

Answer: (C)

Solution

The probability of at least one head in

n

tosses is

1 - (\frac{1}{2})^{n}

, the complement of all tails. We need

1 - \frac{1}{2 ^{n}} \geq \frac{9}{10}

, that is

\frac{1}{2 ^{n}} \leq \frac{1}{10}

, or

2^{n} \geq 10

. Since

2^{3} = 8 < 10

and

2^{4} = 16 \geq 10

, the smallest number of tosses is

4

JEE Main · 2019 · 08 Apr 2019 · Shift 2 · Single correct option