3. Two coins are tossed together. Find the probability of getting (1) two tails Three coins are tossed together Find the probability of getting (1i) atleast one tail (iii) no tail .
Answers
When three coins are tossed together, the total number of outcomes =8
i.e., (HHH,HHT,HTH,THH,TTH,THT,HTT,TTT)
Solution (i):
Let E be the event of getting exactly two heads
Therefore, no. of favorable events, n(E)=3(i.e.,HHT,HTH,THH)
We know that, P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
8
3
Solution (ii):
Let F be the event of getting atmost two heads
Therefore, no. of favorable events, n(E)=7(i.e.,HHT,HTH,TTT,THH,TTH,THT,HTT)
We know that, P(F) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
8
7
Solution (iii):
Let H be the event of getting at least one head and one tail
Therefore, no. of favorable events, n(H)=6(i.e.,HHT,HTH,THH,TTH,THT,HTT)
We know that, P(H) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
8
6
=
4
3
Solution (iv):
Let I be the event of getting no tails
Therefore, no. of favorable events, n(I)=1(i.e.,HHH)
We know that, P(H) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
8
1