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.

(ii) 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.

Sol. When a die is thrown

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 event of getting a prime number

R = { 2, 3, 5 }

∴  n (R) = 3

Here P ∩ Q = ϕ and P U Q = S

∴  P and Q are complementary events.