Three unbiased coins are tossed together. Find the probability of getting: (i) all heads. (ii) exactly two head.
Three unbiased coins are tossed together. Find the probability of getting:
(i) all heads.
(ii) exactly two head.
(iii) exactly one heads.
(iv) at least two heads.
(v) at least two tails.
1 Answers
Elementary events associated to random experiment of tossing three coins are
HHH , HHT, HTH ,THH , HTT,THT,TTH ,TTT
Total number of elementary events = 8.
(i) The event getting all heads is said to occur, if the elementary event HHH occurs, i.e.HHH is an outcome.
Favourable number of elementary events = 1
Hence, required probability =1/8
(ii) The event "getting two heads" will occur, if one of the elementary events HHT, THH, HTH occurs.
Favourable number of elementary events =3
Hence, required probability=3/8
(iii) The event of "getting one head", when three coins are tossed together, occurs if one of the elementary events HTT, THT, TTH, occurs.
Favourable number of elementary events = 3
Hence, required probability=3/8
(iv) If any of the elementary events HHH, HHT, HTH, and THH is an outcome, then we say that the event "getting at least two heads" occurs.
Favourable number of elementary events = 4
Hence, required probability=4/8=1/2.
(v) Similar as (iv) P (getting at least two tails)=4/8=1/2.