Question

A coin is tossed 3 times. Find the sample space of the experiment, what is the probability of "at least two heads", name a different event with the same probability as " at least two heads."

Answer 1

Given:

A coin is tossed 3 times.

To find the probability of getting at least two heads:

First, we write the sample space.

`\begin{gathered} S=\mleft\lbrace\text{HHH, HHT, HTH, THH, HTT, TTH, THT, TTT}\mright\rbrace \\ n(S)=8 \end{gathered}`

A be the event of getting at least two heads.

`\begin{gathered} A=\mleft\lbrace\text{HHH, HHT, HTH, THH}\mright\rbrace \\ n(A)=4 \end{gathered}`

So, the probability of getting at least two heads is

`\begin{gathered} P(A)=(n(A))/(n(S)) \\ =(4)/(8) \\ =(1)/(2) \end{gathered}`

Hence, the probability is,

`(1)/(2)`

The event of getting at least two tails is also getting the same probability as at least two heads.