When 3 coins are tossed simultaneously, all possible outcomes are HHH, HHT, HTH, THH, HTT, THT, TTH, TTT.
Total number of possible outcomes = 8.
(i) Let E1 be the event of getting exactly 2 heads.
Then, the favourable outcomes are HHT, HTH, THH.
Number of favourable outcomes = 3.
∴ P(getting exactly 2 heads) = P(E1)=
3
8
.
(ii) Let E2 be the event of getting at least 2 heads.
Then, E2 is the event of getting 2 or 3 heads.
So, the favourable outcomes are
HHT, HTH, THH, HHH.
Number of favourable outcomes = 4.
∴ P(getting at least 2 heads) = P(E2)=
4
8
=
1
2
.
(iii) Let E3 be the event of getting at most 2 heads.
Then, E3 is the event of getting 0 or 1 head or 2 heads.
So, the favourable outcomes are
TTT, HTT, THT, TTH, HHT, HTH, THH.
Number of favourable outcomes = 7.
∴ P(getting at most 2 heads ) = P(E3)=
7
8
.
