Answer to Question #323486 in Statistics and Probability for Dan

Question

Consider the random event of tossing four coins once, then follow these steps:

1. List all the possible outcomes using the tree diagram.

2. Determine the sample space.

3. Determine the possible values of the random variables.

4. Assign probability values P(X) to each of the random variable.

5. Construct a probability histogram to describe the P(X).

Answer the following guide questions:

1. How many possible outcomes are there?

2. What composes the sample space?

3. How will you describe the histogram?

Answer 1

1. sample space will be;

{HHHH,HHHT,HHTH,HHTT,HTHH,HTHT,HTTH,HTTT,THHH,THHT,THTH,THTT,TTHH,TTHT,TTTH,TTTT}

3 The possible outcomes are head and tail. Assuming that it is an unbiased coin, the random variable for head and tail will be equal.. Let X denote the variable for the number of heads obtained.

The possible values for the random variable are, {0,1,2,3,4}.

$Probability=Number\ of \ hearts (X)/\sum Number \ of \ hearts$

4

5

There are 16 possible outcomes.

The sample space of a random experiment is the collection of all possible outcomes.

Histogram of normal distribution with one maximum.