The recent school question and answer enquired students to say what they agree to is the main important challenge for a student to do in order for you to gain success. Of many results, the one which that stood out was practice. Persons who surely are successful do not become successful by being born. They work hard and determination their lives to succeeding. This is how you can reach your goals. following are one of the answer and question example that you can potentially utilise to practice and develop your information and also give you insights that could just help you to keep up your study in school.

## Question:

8) At the school carnival, Mike will play a game in which he will toss a penny, a nickel, and a dime at the same time. He will be awarded 3 points for each coin that lands with heads faceup. Let the random variable x represent the total number of points awarded on any toss of the coins. What is the expected value of x?

## Answer:

The **expected** **value **of X representing the **average **of the **total** **number **of points awarded on **toss **of the **coins **is 27/8

### How to find the mean (expectation) of a random variable?

Supposing that the considered **random variable **is **discrete**, we get:

where is its n **data values**

and is the **probability** of

### How to calculate the probability of an event?

Suppose that there are **finite elementary events **in the **sample** **space **of the considered **experiment**, and all are equally likely.

Then, suppose we want to find the **probability **of an **event **E.

Then, its **probability **is given as

where **favorable cases **are those **elementary events **who belong to E, and total cases are the size of the **sample space**.

For this case, we’re given that:

- 3
**coins tossed**, and its 3 points on each head**outcome** - X = total number of
**points awarded**

Now, X can have total 4 values, viz 0, 1, 2, and 3

Their each’s **probability **is evaluated as:

- Case 1: No
**heads**

That means all 3 **coins **needs to land on tail.

There is, therefore, single way to do so. Whereas, total **outcomes **possible are (by **product rule**,** **as there are 2 outcomes possible for each **coin**)

Thus, we get:

- Case 2:
**Single head**

When single head, that means 3 points, or X = 3

Total **outcomes possible **= 8,

**Single head **can occur in 3 different ways, as other two needs to be strictly **tails**.

Thus,

- Case 3: Two
**heads**

Two heads means 3+3 = 6 points, or X = 6

Total **outcomes possible **= 8

Two **heads **means **single tail**. Single tail can occur in 3 different ways.

Therefore,

- Case 4:
**Three heads**

Three heads means 3+3+3 = 9 points, or X = 9

Total outcomes **possible **= 8

Three **heads **means no **tail**, only single way to do it.

Thus,

Therefore, the **expectation** of X is calculated as:

Thus, the **expected value **of X is 27/8.

Learn more about **expectation **here:

From the answer and question examples above, hopefully, they might be able to assist the student sort out the question they had been looking for and observe of all the things declared in the answer above. You could actually then have a discussion with your classmate and continue the school learning by studying the problem as a group.