Question

Three different coins are tossed together find the probability of .
i) Exactly two heads ii) At least one tails
ii) Almost two heads iv) At most two tails
v) At least two tails vi) At most one head
vii) At least one head

Answer 1

Total possible outcomes are

$TTT,TTH,THT,THH,HTT,HTH,HHT,HHH$

Number of total possible outcomes= $8$

i) Exactly two heads

$THH,HTH,HHT$

$=\frac{3}{8}$

ii) At least one tails

$THH,HTH,HHT$

$=\frac{3}{8}$

iii) Almost two heads

$THH,HTH,HHT,HHH$

$=\frac{4}{8}=\frac{1}{2}$

iv) At most two tails

$TTT,TTH,THT,HTT$

$=\frac{4}{8}=\frac{1}{2}$

v) At least two tails

$TTH,THT,HTT$

$=\frac{3}{8}$

vi) At most one head

$TTH,THT,THH,HTT,HTH,HHT$

$=\frac{6}{8}=\frac{3}{4}$

vii) At least one head

$TTH,THT,HTT$

$=\frac{3}{8}$