Three coins are tossed together. Find the probability of getting:
(i) exactly two heads
(ii) at least two heads
(iii) at least one head and one tail
(iv) no tails

Explanation

Total Possible outcomes when three coins tossed together
`"(TTT,TTH,THT,THH,HTT,HTH,HHT,HHH)"`

total outcomes `= 8`

1) Favourable outcome for getting exactly two heads:`"HHT,HTH,THH" = 3`
Probability of getting exactly two heads `= 3/8`

(b)at most two heads
Favourable conditions `"=TTT,TTH,THT,THH,HTT"`
`"HTH,HHT" = 7`
Probability of getting at most two heads `= 7/8`

c)at least one head and one tail:
Favourable conditions:`TTH,THT,THH,HTT`
`HTH,HHT= 6`
Probability of getting at least one head and one tail `= 6/8 = 3/4`

d)no tails:
Favourable conditions:`HHH = 1`
Probability of getting no tails `= 1/8`