If the outcomes of an experiment have values E_{1}, E_{2},
E_{3}, E_{4}, . . . , E_{n},

Then the **Expected Value** of the experiment is

E_{1}●P(E_{2}) +
E_{3}●P(E_{4}) + E_{5}●P(E_{6})
+ . . . . +E_{n}●P(E_{n})

In other words . . . .

*Expected Value = Sum of all the products of the outcomes multiplied
by their respective probabilities.*

**
**__Calculate Expected Gross Winnings of a Lottery Ticket__

__
____Example__ Calculate the expected gross winnings for the
$1 BIG BEAR ticket with probabilities given below.

Prize Probability

$1 prize with probability 1/10

$2 prize with probability 1/10.64

$3 prize with probability 1/20

$10 prize with probability 1/166.67

$20 prize with probability 1/500

$30 prize with probability 1/750

$500 prize with probability 1/60,000

$5,000 prize with probability 1/240,000

The expected gross winnings are obtained by adding all of the
products of the prize multiplied by the probability. This is calculated
as

$1 × 1/10 + $2 × 1/10.64 + $3 × 1/20 + $10 × 1/166.67 +

$20 × 1/500 + $30 × 1/750 + $500 × 1/60,000 + $5,000 × 1/240,000

This may be input into a scientific calculator as

1 ÷ 10 + 2 ÷ 10.64 + 3 ÷
20 + 10 ÷ 166.67 + 20 ÷ 500
+ 30 ÷ 750 + 500 ÷ 60,000 +
5,000 ÷ 240,000 =

The expected gross winnings are $0.607 which rounds to $0.61 .

Thus, for each $1 ticket you purchase, you can expect to win 61 cents
back on the average. You can, however, expect to lose a net 39 cents on
each ticket.

**Expected Winnings of a Lottery Ticket**

The **expected gross winnings** of a lottery ticket is equal to
the *average* gross amount that a person will win for each ticket
purchased.

__
____Example__ If the expected gross winnings of a $1 lottery
ticket are $0.56, how much money will a person win expect to win by
purchasing 1000 lottery tickets?

Since the person wins $0.56 per ticket, the person could expect to
win 1000 x $0.56 = $560 by purchasing 1000 tickets. The expected net
winnings are not $560 however since the 1000 tickets cost $1000.

By factoring in the purchase price, the net expected *loss* is
$560 - $1000 = ($440).

Note that expected gross winnings do not indicate the actual amount
of money but the *expected* amount of money that a person will win.
The person could purchase the “big-winner” ticket and win much more than
$560. Also, the person could win less than $560. Expected gross winnings
merely indicates the “average” gross amount a person will win.

Lottery ticket “facts” are given here.