A coin is tossed three times, consider the followingevents.A : No head appears, B: Exactly one head appearsand C: Atleast two appear.Do they form a set of mutually exclusive andexhaustive events?

A coin is tossed three times, consider the followingevents.A : No head

1.	A coin is tossed three times, consider the followingevents.A : No head appears, B: Exactly one head appearsand C: Atleast two appear.Do they form a set of mutually exclusive andexhaustive events?
Answer» The sample space of the experiment is `S = {HHH,HHT,HTH,THH,HT T,THT,T TH,T T T}` `A = {T T T}` `B = {HT T, THT, T TH}` `C = {HHT, HTH, THH, HHH}` Now, `A uu B uu C = {T T T, HT T, THT, T TH, HHT, HTH, THH, HHH} = S` Therefore, A, B and C are exhaustive events. Also, `A nn B = phi, A nn C = phi and B nn C = phi` Therefore, A, B and C form a set of mutually exclusive and exhaustive events.

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A coin is tossed three times, consider the followingevents.A : No head appears, B: Exactly one head appearsand C: Atleast two appear.Do they form a set of mutually exclusive andexhaustive events?

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