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
• B. S&R AND R&T
• C. S&R AND S&T
• D. S&T ONLY

Answer 1

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.