Straight Lines

Question
CBSEENMA11014632

Three coins are tossed. Describe two events which are not mutually exclusive. 

Solution

Three coins are tossed.
rightwards double arrow The sample space is: S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
Event E = at least two heads show
rightwards double arrow    E = {HHH, HHT, HTH, THH}
 Event F = exactly two heads show
            = {HHT, HTH, THH}
Now, straight E intersection straight F equals space left curly bracket HHH comma space HTH comma space THH comma space HHT right curly bracket space intersection space left curly bracket HHT comma space HTH comma space THH right curly bracket
                = {HHT, HTH, THH} not equal to straight ϕ
Hence, E and F are not mutually exclusive.