Question

A coin is tossed and a die is thrown simultaneously:
P is the event of getting head and a odd number.
Q is the event of getting either H or T and an even number.
R is the event of getting a number on die greater than 7 and a tail.

Answer 1

Given:
A coin is tossed and a die is thrown simultaneously.
We have:
Sample space = {H₁, H₂, H₃, H₄, H₅, H₆, T₁, T₂, T₃, T₄, T_5, T₆}
∴ n(S) = 12
Now,
P is the event of getting a head and an odd number.
P = {H₁, H₃, H₅}
∴ n(P) = 3

Q is the event of getting either a head or a tail and an even number.
Q = {H₂, H₄, H₆, T₂, T₄, T₆}
∴ n(Q) = 6

R is the event of getting a number greater than 7 on the die and a tail.
In the sample space, there is no event in which the number on the upper face of the die is greater than 7.
R is an impossible event.
R = {} = $\mathrm{\varphi }$
n(R) = 0
$\mathrm{Here},P\cap Q=\mathrm{\varphi }\mathrm{but}\mathrm{P}\cup \mathrm{Q}\ne \mathrm{S}$
So, events P and Q are mutually exclusive but not complementary.
$\mathrm{P}\cap \mathrm{R}=\mathrm{\varphi }$
So, events P and R are mutually exclusive.
$\mathrm{Q}\cap \mathrm{R}=\varphi$
So, events Q and R are mutually exclusive.