Question

Tossing coins Imagine tossing a fair coin $3$ times. (a) What is the sample space for this chance

process? (b) What is the assignment of probabilities to outcomes in this sample space?

Short answer

Part (a) All potential outcomes sequences$=2^3$.

Part (b) The probability$=\frac{1}{8}$

Step-by-step solution

Part (a) Step 1. Given Information  

No. of times coin is tossed$=3$.

Part (a) Step 2. Concept Used 

A chance process' sample space$S$ is the collection of all potential outcomes. A probability model is a two-part description of a random process that includes a sample space$S$ and probabilities for each result.

Part (a) Step 3. Calculation  

The possible ordered outcomes are listed as elements in a sample space, which is commonly indicated using set notation. A sequence of three fair coins' sample space contains all conceivable outcomes sequences$=2^3$

To put it another way, the sample of a fair coin is $\left\{H,T\right\}$

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

Part (b) Step 1. Calculation  

A sequence of three fair coins' sample space contains all conceivable outcomes sequences$=2^3$

To put it another way, the sample of a fair coin flip is $\left\{H,T\right\}$

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

Because there are $8$possible outcomes in the specified sample space, a fair coin is tossed three times. As a result, all of the events in the specified sample space have the same probability. As a result, the likelihood $=\frac{1}{8}$.