Question

Probability question please follow the comment

how do we use general inclusion and exclusion theorem to derive 4 to 5 events?

for example 3 events are that AUB=A+B-(A intersect B), but how about 4 and 5? Please you need to show me the step rather than paste the inclusion and exclusion formula and explain

Answer 1

(1) For 4 Events: A, B, C and D:

Step 1:

All singletons:

A + B + C + D

Step 2:

All pairs:

Step 3:

All Triplets:

Step 4:

All Quadruples:

Step 5:
Step 1 - Step 2 + Step3 - Step 4: we get the Inclusion and Exclusion Theorem for 4 Events: A, B, C and D as follows:

A + B + C + D

(2) For 5 Events: A, B, C, D and E:

Step 1:

All singletons:

A + B + C + D + E

Step 2:

All pairs:

Step 3:

All Triplets:

Step 4:

All Quadruples:

Step 5:

All 5 values:

Step 6:
Step 1 - Step 2 + Step3 - Step 4 + step 5: we get the Inclusion and Exclusion Theorem for 4 Events: A, B, C, D and E as follows:

= A + B + C + D + E