Question

Three fair quarters are tossed, and a tail appears on at least one of them. What is the probability that at least one head appears? Express your answer as a common fraction

Answer 1

Answer:

Probability that at least one head appears is$\frac{6}{7}$

Step-by-step explanation:

Given : Three fair quarters are tossed, and a tail appears on at least one of them.

To find : What is the probability that at least one head appears?

Solution :

When three fair quarters are tossed the sample form is

$\{HHH,HHT,HTH,HTT,THH,THT,TTH,TTT\}$

According to question,

In a sample space a tail appears on at least one of them.

i.e. Total outcomes is $\{HHT,HTH,HTT,THH,THT,TTH,TTT\}=7$

Favorable outcome is getting at least one head appears

i.e. Favorable outcome is $\{HHT,HTH,HTT,THH,THT,TTH\}=6$

Probability that at least one head appears is

$\text{Probability}=\frac{\text{Favorable outcome }}{\text{Total outcome}}$

$\text{Probability}=\frac{6}{7}$

Therefore, Probability that at least one head appears is$\frac{6}{7}$