Question

When a penny is flipped two times, the probability of flipping exactly one tail is__?

Answer 1

Answer:

$P(Tail = 1) = \frac{1}{2}$

Step-by-step explanation:

Given

$Flips = 2$

Required

Probability of exactly one tail

This event can be represented as:

(Head and Tail) or (Tail and Head)

In the flip of a coin (penny), the following probabilities exist:

$P(Head) = \frac{1}{2}$

$P(Tail) = \frac{1}{2}$

So, the required probability is:

$P(Tail = 1) = (P(Head) * P(Tail)) + (P(Tail) * P(Head))$

Substitute values for P(Head) and P(Tail)

$P(Tail = 1) = (\frac{1}{2}*\frac{1}{2}) + (\frac{1}{2}*\frac{1}{2})$

$P(Tail = 1) = (\frac{1}{4}) + (\frac{1}{4})$

$P(Tail = 1) = \frac{1}{4} + \frac{1}{4}$

Take LCM

$P(Tail = 1) = \frac{1+1}{4}$

$P(Tail = 1) = \frac{2}{4}$

$P(Tail = 1) = \frac{1}{2}$