# Probability of the Union of 4 events

• Jan 30th 2011, 03:58 PM
divinelogos
Probability of the Union of 4 events
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 \$\displaystyle \cap\$ D) + P(E \$\displaystyle \cap\$ N) +P (E \$\displaystyle \cap\$ B) + P(D \$\displaystyle \cap\$ N) + P(D \$\displaystyle \cap\$ B +[P(N \$\displaystyle \cap\$ B] +

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

4. P( E \$\displaystyle \cap\$ D\$\displaystyle \cap\$ N \$\displaystyle \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 :)
• Jan 30th 2011, 04:15 PM
dwsmith
Quote:

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

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

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