Probability of the Union of 4 events

**divinelogos** · January 30th 2011, 03:58 PM

What is the probability of the union of 4 events? The events are:

E- hitting an even number on a dartboard= .0249

D- hitting a double P=.1049

N- hitting a number higher than 10 P=.0249

B- hitting a bullseye P= .007

I came up with:

1. P(E)+P(D)+P(N)+P(B) -

2. [P (E $\cap$ D) + P(E $\cap$ N) +P (E $\cap$ B) + P(D $\cap$ N) + P(D $\cap$ B +[P(N $\cap$ B] +

3. P(E $\cap$ D $\cap$ N)]+ P(D $\cap$ N $\cap$ B)] -

4. P( E $\cap$ D $\cap$ N $\cap$ B)

I'm basically asking if I got the formula right for the probability of the union of 4 events.

Any help is appreciated

**dwsmith** · January 30th 2011, 04:15 PM

Originally Posted by divinelogos

What is the probability of the union of 4 events? The events are:

E- hitting an even number on a dartboard= .0249

D- hitting a double P=.1049

N- hitting a number higher than 10 P=.0249

B- hitting a bullseye P= .007

I came up with:

1. P(E)+P(D)+P(N)+P(B) -

2. [P (E $\cap$ D) + P(E $\cap$ N) +P (E $\cap$ B) + P(D $\cap$ N) + P(D $\cap$ B +[P(N $\cap$ B] +

3. P(E $\cap$ D $\cap$ N)]+ P(D $\cap$ N $\cap$ B)] -

4. P( E $\cap$ D $\cap$ N $\cap$ B)

I'm basically asking if I got the formula right for the probability of the union of 4 events.

Any help is appreciated

$\displaystyle P(A\cup B\cup C\cup D)=P(A)+P(B)+P(C)+P(D)-P(A\cap B)-P(A\cap C)-P(A\cap D)-P(B\cap C)-$ $\displaystyle P(B\cap D)-P(C\cap D)+P(A\cap B\cap C)+P(A\cap B\cap D)+P(B\cap C\cap D)-P(A\cap B\cap C\cap D)$

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