**(vi) 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.**

**Sol. **A coin is tossed and a die is thrown

S = { H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6 }

∴ n (S) = 12

P is the event of getting head and an odd number

P = { H1, H3, H5 }

∴ n (P) = 3

Q is the event of getting either H or T 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 and tail 1

R = { }

∴ n (R) = 0

Here, P∩Q = ϕ

∴ P and Q are mutually exclusive events.

Q ∩R = ϕ

∴ Q and R are mutually exclusive events.

P ∩R = ϕ

∴ P and R are mutually exclusive events.

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