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

P(A υ B) = P(A) + P(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.
      Y = event when a yellow card is chosen.
The sample space, S = 12, n(S) = 12
n(G) = 4 and n(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.
GY= P(GY)= P(G)+P(Y)                = 4 12 + 5 12                = 9 12 = 3 4