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

Probability that at least one head appears is
`(6)/(7)`

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}=(6)/(7)`

Therefore, Probability that at least one head appears is
`(6)/(7)`