Three unbiased coins are tossed together. Find the probability of getting:

all heads             
(ii)   two heads
one head            
(iv)   at least two heads

Explanation

Three unbiased coins are tossed together.
Sample space,`S = {HHH, HHT, HTH, THH, T TH, THT, HTT, TT T}`
Number of events, `n(S) = 8`
(i)For getting one head, we will have the event space,
`S₁ = {TTH, THT, HTT}`
Number of events, `n(S₁) = 3`
Thus, probability of getting one head
`P(S₁) = 3/8`
(ii)For getting two heads, we will have the event space,
`S₂ = {HHT, HTH, THH}`
Number of events, `n(S₂) = 3`
Thus, probability of getting two heads
`P(S₂) = 3/8`
(iii)For getting all heads, we will have the sample space,
`S₃ = {HHH}`
Number of events, `n(S₃) = 1`
Thus, probability of getting all heads
`P(S₃) = 1/8`
(iv)For getting at least two heads, we will have the sample space,
`S₄ = {HHH, HHT, HTH, THH}`
Number of events, `n(S₄) = 4`
Thus, probability of at least two heads
`P(S₄) = 1/2`