A coin is tossed three times, consider the following events– E1: No

1.	A coin is tossed three times, consider the following events– E1: No head appears E2 : Exactly one heat appear E3: Atleast one head appears Do they from a set of mutually exclusive and exhaustive events?
Answer» When a coin is tossed three times, the sample space is– S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} E₁ = {TTT} E₂ = {HTT, THT, TTH} E₃ = {HHH, HHT, HTH, HTT, THH, THT, TTH} E₁ ∩ E₂ = ϕ , E₁ ∩ E₃ = ϕ , E₂ ∩ E₃ = {HTT, THT, TTH} ≠ ϕ Also, E₁ ∩ E₂E₃ = S. ∴ E₁, E₂, E₃ are not mutually eclusive but they are exhaustive events.

A coin is tossed three times, consider the following events– E1: No head appears E2 : Exactly one heat appear E3: Atleast one head appears Do they from a set of mutually exclusive and exhaustive events?

Answer»

When a coin is tossed three times, the sample space is–

S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

E₁ = {TTT}

E₂ = {HTT, THT, TTH}

E₃ = {HHH, HHT, HTH, HTT, THH, THT, TTH}

E₁ ∩ E₂ = ϕ , E₁ ∩ E₃ = ϕ , E₂ ∩ E₃ = {HTT, THT, TTH}

≠ ϕ

Also, E₁ ∩ E₂E₃ = S.

∴ E₁, E₂, E₃ are not mutually eclusive but they are exhaustive events.

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A coin is tossed three times, consider the following events– E1: No head appears E2 : Exactly one heat appear E3: Atleast one head appears Do they from a set of mutually exclusive and exhaustive events?

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