Need up to 30 seconds to load.

so let's begin by organizing the data in

this problem in a form of a table so

first we're gonna write the outcomes

there's really only two outcomes that we

need to be concerned with either she

wins the game or she loses now the next

thing needs to concern ourselves with is

the value of each outcome if she wins

the game she receives $500 if she loses

the game well the cost of plays a

hundred so she's gonna lose a hundred

dollars the next thing is the

probability of each outcome the

probability of Lisa winning the game is

twenty percent according to the problem

based on that what is the probability

that she's gonna lose well we know that

the maximum probability is a hundred

percent so there's a twenty percent

chance that she's gonna win the game

there's an 80 percent chance that she

will lose the game since there's only

two outcomes so now we have enough

information to calculate the expected

value for winning in this game so this

is going to be number one and this is

number two

so x 1.is the value of winning the game

that's going to be 500 dollars P one is

the probability of winning so we need to

convert the percentage into a decimal to

convert percent to a decimal divided by

a hundred or you can move the decimal

point two units to the left so 20

percent as a decimal is point two zero

now X two is the value of losing the

game in this case that is negative 100 P

two is the probability of losing which

is eighty percent or 0.8 zero

now 500 times point 20 that is 100 and

negative 100 times point 80 is negative

80 so the expected value of when in a

game on average is $20 so on average if

she continues to play this game she can

earn twenty dollars for a game now how

much would she expect to win let's say

if she were to play ten games well if

she can average twenty dollars per game

and then ten games would at this rate

give her an expected earnings of $200 if

she would have played a hundred games

based on this average earnings she would

expect to have a total of 2,000 at that

point and so that's how you can

calculate expected value for winning a

single game and then you could use that

to estimate what your total earnings

will be for playing a certain number of

games now let's work on another example

problem company XYZ generates a profit

of 40 dollars for each laptop that they

sell the company loses 500 dollars for

every laptop that is returned due to

some defect if three out of every

laptops or let me say that again if

three out of every 100 laptops that they

produce is defective

what is the expected value of profit per

laptop well let's write down what we

know so in this problem similar to the

last one there's only two outcomes that

we need to be concerned with either the

company makes a working laptop or a

defective one so let's say if they

generate a working laptop that's a win

for them and if they make a defective

laptop that's basically a loss for them

so the value of making a laptop that is

functioning properly

is $40 that's how much they're gonna

profit for each properly working laptop

that they sell now if they make a

defective laptop they're gonna lose $500

that's a huge loss it takes a lot of

money to make a laptop and now the

probability of making a working laptop

well let's find the probability of

making a defective laptop three out of

every 100 laptops that they produce is

defective so that means that there's a

three percent chance of making a

defective laptop which means there's a

97% chance of making a laptop that is

working properly so with this

information we can calculate the

expected value of profit for each laptop

so using the same formula x1 + p1 + x2

p2 it's gonna be $40 for making a laptop

that works properly times the

probability of making such a laptop

which is 0.97 and then + X 2 which is

negative 500 times the probability of

making a defective laptop which is point

zero three so 4 times point I mean 40

times point 97 that is thirty eight

point eight and negative 500 times point

zero three is negative 15

subtracting the two numbers we get 23.8

so the expected value of profit per

laptop is $23.80

so this means that for every laptop that

they sell the expected profit is $23.80

so if they were to sell a hundred

laptops they can expect a profit of

23.82 times one hundred or two thousand

three hundred and eighty dollars but the

answer that we're looking for in this

video the expected value of profit per

one laptop is $23.80 so now you know how

to calculate the expected value in a

variety of different situations thanks

for watching