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
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.