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.


(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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