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A coin is tossed three times, consider t...

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

Text Solution

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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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