7.3 Probability of Mutually Exclusive Events


7.3 Probability of Mutually Exclusive Events
1. Two events are mutually exclusive if they cannot occur at the same time.
 


2.
If A and B are mutually exclusive events, then

(A υ B) = (A) + (B)
Example:
A bag contains 3 blue cards, 4 green cards and 5 yellow cards. A card is chosen at random from the box. Find the probability that the chosen card is green or yellow.


Solution:
Let G = event when a green card is chosen.
  = event when a yellow card is chosen.
The sample space, S = 12, (S) = 12
(G) = 4 and (Y) = 5

P ( G ) = n ( G ) n ( S ) = 4 12 P ( Y ) = n ( Y ) n ( S ) = 5 12

Events G and Y cannot occur simultaneously because we cannot obtain green card and yellow card at the same time. Therefore, events G and Y are mutually exclusive.

G Y = P ( G Y ) = P ( G ) + P ( Y ) = 4 12 + 5 12 = 9 12 = 3 4

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