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?

A
R&T ONLY
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B
S&R AND R&T
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C
S&R AND S&T
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D
S&T ONLY
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Solution

## The correct option is C S&R AND S&TLet'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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