A fair coin is tossed three times. What is the probability of tossing at least two tails?

1. Problem Description

A fair coin is tossed three times. What is the probability of tossing at least two tails?

2. Solution Steps

Let's list all possible outcomes when tossing a fair coin three times:

HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.

There are a total of $2^3 = 8$ possible outcomes.

We want to find the probability of getting at least two tails. This means we want to find the outcomes with two tails or three tails.

Outcomes with two tails are: HTT, THT, TTH. There are 3 such outcomes.

Outcomes with three tails are: TTT. There is 1 such outcome.

The total number of outcomes with at least two tails is $3 + 1 = 4$.

The probability of getting at least two tails is the number of favorable outcomes divided by the total number of possible outcomes.

$P(\text{at least two tails}) = \frac{\text{Number of outcomes with at least two tails}}{\text{Total number of outcomes}}$

$P(\text{at least two tails}) = \frac{4}{8} = \frac{1}{2}$

3. Final Answer

The probability of tossing at least two tails is $\frac{1}{2}$.