# Likelihood of event merging

## Event Merge Formula

P (E1 or E2) = P (E1) + P (E2) - P (E1 and is2)

In fact, if there are elements common to E1 and is2, these events will be computed in the calculation of P (E1) and P (E2).

To be considered once, we subtract P (E1 and is2).

## Formula for probability of mutually exclusive event joining

P (E1 or E2 or E3 or… or Eno) = P (E1) + P (E2) +… + P (Eno)

Example: If two dice, blue and white, are rolled, what is the probability of going out 5 in blue or 3 in white?

Considering the events:

A: Take 5 on blue die and P (A) = 1/6

B: Take 3 on white die and P (B) = 1/6

S being the sample space of all possible results, we have:

n (S) = 6.6 = 36 possibilities. Hence we have: P (A or B) = 1/6 + 1/6 - 1/36 = 11/36

Example: If we randomly pull out a 52-card playing card, what is the probability of being an 8 or a King?

S being the sample space of all possible outcomes, we have: n (S) = 52 letters. Consider the events:

A: Exit 8 and P (A) = 4/52

B: leave a king and P (B) = 4/52

Thus, P (A or B) = 4/52 + 4/52 - 0 = 8/52 = 2/13.

Note that P (A and B) = 0, since a card cannot be 8 and king at the same time. When this occurs we say that events A and B are mutually exclusive.

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