# Expected Value

See how to find the expected value of an event.

2 examples and their solutions.

## Expected Value

### Formula

E(X) = x

x_{1}p_{1}+ x_{2}p_{2}+ x_{3}p_{3}+ ..._{i}: Result value of an event i

p

_{i}: Probability of an event i

p

_{1}+ p

_{2}+ p

_{3}+ ... = 1

### Example

A coin is tossed once.

If you get a head, you get 2 points.

If you get a tail, you lose 1 point.

Find the expected value of the points.

Solution If you get a head, you get 2 points.

If you get a tail, you lose 1 point.

Find the expected value of the points.

1) Head

x

p

2) Tail

x

p

E(X) = 2⋅12 + -1⋅12

= 1 - 12

= 12 - [3]

x

_{1}= 2p

_{1}= 12 - [1]2) Tail

x

_{1}= -1p

_{2}= 12 - [2]E(X) = 2⋅12 + -1⋅12

= 1 - 12

= 12 - [3]

[1]

Probability of getting a head

[2]

Probability of getting a tail

[3]

This means if you toss a coin once,

you expect to get 1/2 points.

you expect to get 1/2 points.

Close

### Example

For the given spinner,

if you spin the arrow once,

find the expected value of the points.

Solution if you spin the arrow once,

find the expected value of the points.

E(X) = 1⋅38 + 2⋅38 + 3⋅28

= 3 + 6 + 68

= 9 + 68

= 158

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