Question

Example &
A coin is tossed three times, consider the following events.
A: 'No head appears', B: 'Exactly one head appears' and C: 'Atleast two heads
appear'.
Do they form a set of mutually exclusive and exhaustive events?​

Answer 1

Explanation:

A={(T,T,T)}, B={(H,T,T),(T,H,T),(T,T,H)} and C={(H,H,T),(T,H,H),(H,T,H),(H,H,H)}

∴(A∪B)∩(A∪C)

={(T,T,T),(H,T,T),(T,H,T),(T,T,H)}∩{(T,T,T),(H,H,T),(T,H,H),(H,T,H),(H,H,H)}

={(T,T,T)}=A

∴(A∩B

′

)∪(A∩C

′

)

={(H,H,T),(T,H,H),(H,T,H),(H,H,H)}∪{(T,T,T),(H,T,T),(T,H,T),(T,T,H)}=B

′

∪C

′

∴A∩B∩(B

′

∪C

′

)

={(T,T,T)}∩{(H,T,T),(T,H,T),(T,T,H)}∩{(T,T,T),(H,T,T)

,(T,H,T),(T,T,H),(H,H,T),(T,H,H),(H,T,H),(H,H,H)}

=ϕ

∴A∩(B

′

∪C

′

)

={(T,T,T)}∩{(H,H,T),(T,H,H),(H,T,H),(H,H,H),(T,T,T),(H,T,T),(T,H,T),(T,T,H)}

={(T,T,T)}=A