The standard deviation of the number of tails in three tosses of a coin is: Option 1: 3/4 Option 2: 3/2 Option 3: 3/√2 Option 4: √3/2

Answer: √3/2. Solution: The number of tails in three tosses of a coin follows a binomial distribution. For each toss: - Two outcomes: Head or Tail - Independent tosses - Constant probability The parameters are: n = 3 (number of tosses) p = 1/2 (probability of getting tails) q = 1/2 (probability of getting heads) For a binomial distribution, the standard deviation is: = √npq = √(3 x 1/2 x 1/2) = √(3 x 1/4) = √(3/4) = √3/√4 = √3/2 Therefore, the standard deviation of the number of tails in three tosses of a coin is √3/2.

Algebra

Probability

Medium

applied

The standard deviation of the number of tails in three tosses of a coin is:

$\frac{3}{4}$

$\frac{3}{2}$

$\frac{3}{\sqrt{2}}$

$\frac{\sqrt{3}}{2}$

✅ Correct Option: 4

The number of tails in three tosses of a coin follows a binomial distribution.

For each toss:

Two outcomes: Head or Tail
Independent tosses
Constant probability

The parameters are:

$n = 3$ (number of tosses)

$p = \frac{1}{2}$ (probability of getting tails)

$q = \frac{1}{2}$ (probability of getting heads)

For a binomial distribution, the standard deviation is:

$\sigma = \sqrt{npq}$

$\sigma = \sqrt{3 \times \frac{1}{2} \times \frac{1}{2}}$

$\sigma = \sqrt{3 \times \frac{1}{4}}$

$\sigma = \sqrt{\frac{3}{4}}$

$\sigma = \frac{\sqrt{3}}{\sqrt{4}}$

$\sigma = \frac{\sqrt{3}}{2}$

Therefore, the standard deviation of the number of tails in three tosses of a coin is $\frac{\sqrt{3}}{2}$ .

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Solution

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