Question

Three coins are tossed up simultaneously.

R represents the event of getting at least 2 heads.

S represents the event of getting no heads

T represents the event of getting heads on the second coin.

Find the one that is mutually exclusive?

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Solution

The correct option is **C** S&R AND S&T

Let's make sample space of each event.

R = at least two heads

∴ R = {HHT, HTH, THH, HHH}.

Now, for event S.

S = event of getting no head

S = {TTT}

T = event of getting heads on second coin

T = {HHH, THH, THT, HHT}

∴ n(R) = 4, n(s) = 1, n(T) = 4

∴ S & R and S & T are mutually exclusive, as they have nothing in their intersection.

So, option c is correct.

Let's make sample space of each event.

R = at least two heads

∴ R = {HHT, HTH, THH, HHH}.

Now, for event S.

S = event of getting no head

S = {TTT}

T = event of getting heads on second coin

T = {HHH, THH, THT, HHT}

∴ n(R) = 4, n(s) = 1, n(T) = 4

∴ S & R and S & T are mutually exclusive, as they have nothing in their intersection.

So, option c is correct.

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