NCERT Solutions
Class 11 Maths
Probability

Ex.16.3 Q.8
Three coins are tossed once. Find the probability of getting
(1) 3 heads
(2) 2 heads
(3) at least 2 heads
(4) at most 2 heads
(5) no head
(6) 3 tails
(7) exactly two tails
(8) no tail
(9) at most two tails
When three coins are tossed once, the sample space is given by
S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
Accordingly, n(S) = 8
It is known that the probability of an event A is given by
Now, P(A) = Number of outcomes favourable to A ÷ Total number of possible outcomes
= n(A) ÷ n(S)
= 6 ÷ 10
=
(1) Let B be the event of the occurrence of 3 heads. Accordingly, B = {HHH}
So, P(B) = n(B) ÷ n(S) =
(2) Let C be the event of the occurrence of 2 heads.
Accordingly, C = {HHT, HTH, THH}
So, P(C) = n(C) ÷ n(S) =
(3) Let D be the event of the occurrence of at least 2 heads.
Accordingly, D = {HHH, HHT, HTH, THH}
So, P(D) = n(D) ÷ n(S) = =
(4) Let E be the event of the occurrence of at most 2 heads.
Accordingly, E = {HHT, HTH, THH, HTT, THT, TTH, TTT}
So, P(E) = n(E) ÷ n(S) =
(5) Let F be the event of the occurrence of no head.
Accordingly, F = {TTT}
So, P(F) = n(F) ÷ n(S) =
(6) Let G be the event of the occurrence of 3 tails.
Accordingly, G = {TTT}
So, P(G) = n(G) ÷ n(S) =
(7) Let H be the event of the occurrence of exactly 2 tails.
Accordingly, H = {HTT, THT, TTH}
So, P(H) = n(H) ÷ n(S) =
(8) Let I be the event of the occurrence of no tail.
Accordingly, I = {HHH}
So, P(I) = n(I) ÷ n(S) =
(9) Let J be the event of the occurrence of at most 2 tails.
Accordingly, J = {HHH, HHT, HTH, THH, HTT, THT, TTH}
So, P(J) = n(J) ÷ n(S) =