Engineering
Mathematics
Basic Definitions Related to Probability
Question
A die is thrown :
P is the event of getting an odd number.
Q is the event of getting an even number.
R is the event of getting a prime number.
Which of the following pairs is mutually exclusive ?
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Solution
Let S be the sample space S = {1, 2, 3, 4, 5, 6}
n(S) = 6
P is the event of getting an odd number
∴ P = {1, 3, 5} ⟹ n(P) = 3
Q is the event of getting an even number
∴ Q = {2, 4, 6} ⟹ n(Q) = 3
R is the vent of getting a prime number
∴ R = {2, 3, 5} ⟹ n(R) = 3
We have, P = S − Q and Q = S − P
∴ n(P) and n(Q) both are complementary.
Two events are mutually exclusive if they are disjoint
∴ n(P) and n(Q) both are complementary.
Two events are mutually exclusive if they are disjoint
Now, P∩Q = ϕ
⇒ P and Q are disjoint i.e. they don't have common elements.
Hence, P and Q are mutually exclusive.