Introduction:
in statistics help ,Two events are said to be mutually non exclusive when they share one or more of the same outcome. Two or more events can occur simultaneously i.e. the occurrence of one does not prevent the occurrence of other in all cases. If and B are two events that share outcomes in common, mutually non exclusive then
P(A or B) = P(A) + P(B) – P(A and B)
Example:
What is the probability of a die showing an even more than 3 when it is rolled down?
Number of sides in a die = 6
Number of even numbers 2, 4, 6 = 3
Probability of even P(E) = 3/6 = 1/ 2
More than 3 = 4, 5, 6 = 3
Probability for more than 3 = P(M) = 3/6 = 1/ 2
P(E or M) = P(E) + P(M) - P(E and M)
= 1/ 2 + 1/ 2 - (1/ 2 x 1/ 2)
= 1 – 1/ 4 = 3/ 4
The probability of a die showing an even more than 3 is 3/ 4.
Solved Problems
The following solved statistics answers help us to understand the concept .
1) If one card is drawn from deck of cards what is the probability of selecting red color 10 in random.
Number of cards in a card = 52
Number of red color cards = 26
Number of 10’s in a deck = 4
Probability of selecting 10 from a deck = 4/52 = 1/13
Probability of selecting red color = 26/52 = 1/ 2
P(T or R) = P(T) + P(R) - P(T and R)
= 1/ 4 + 1/13 – (1/ 2 x 1/13)
= 17/52 – 1/26
= (17 – 2)/52
= 15/52
Probability of selecting red color 10 in random is 15/52.
2) Find probability of A and B if P(A)=10,p(B)=5,probability of Aor B is 5?
Given:
p(A)=10
p(B)=5
p(A or B)=5
p( A and B)=????
P(A or B) = P(A) + P(B) – P(A and B)
P(A and B) = p(A)+p(B)-p(A or B)
=10+5-5
=10
Related Tags
Mutually Non Exclusive Events in statistics , probability Mutually Non Exclusive Events , Mutually Non Exclusive Events definition