Non-Mutually Exclusive Events(Compatible)
Two or more 'non-mutually exclusive' events can occur at the same time. In every case one event does not prevent the other happening.
The probability of either one OR both events occuring is:
P(A or B) = P(A) + P(B) − P(A ∩ B)
where P(A ∩ B) is the probability of event A AND event B happening at the same time.
What is the probability of getting a black card OR an Ace by drawing one card from a 52 deck.
P(Black) = 26/52
P(Ace) = 4/52
P(Black ∩ Ace) = 2/52
i.e. Black and Ace, the Ace of Clubs & the Ace of Spades
P(Black or Ace) = P(Black) + P(Ace) - P(Black ∩ Ace)
P(Black or Ace) = 26/52 + 4/52 - 2/52
P(Black or Ace) = 28/52 = 7/13
A card can either be Black or Ace or both (i.e. a Black Ace).
So that's why we need to subtract the probability of a card being both Black AND Ace .
This card has already been accounted for in the probability of the card being Black AND the probability of the card being Ace.
For a six sided die, what is the probability of getting an even number OR a number greater than 3 ?
Both events, A and B, occur when either a 4 or 6 are thrown:
A - the event of getting an even number (2, 4, 6)
B - the event of getting a number greater than 3 (4, 5, 6)
P(A) = 3/6
P(B) = 3/6
P(A ∩ B) = 2/6
P(A) or P(B) = P(A) + P(B) - P(A ∩ B)
P(A) or P(B) = 3/6 + 3/6 - 2/6 = 4/6 = 2/3
For a set of dominoes, what is the probability of choosing one domino and it being a 5 or any double?
P(5) = 7/28
P(double) = 7/28
P(5 ∩ double) = 1/28
P(5) or P(double) = P(5) + P(double) - P(5 ∩ double)
P(5) or P(double) = 7/28 + 7/28 - 1/28 = 13/28
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