if there is a probability in getting tails in a single toss i.e. 1/2 then what is the probability of getting 2 tails in two tosses ? explain. if answer is 1/4 then explain how.

Dear Student,

Please find below the solution to the asked query:

We know : Probability  P ( E ) = $\frac{\mathrm{Number} \mathrm{of} \mathrm{desired} \mathrm{events} \mathrm{n} ( \mathrm{E} ) }{\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{events} \mathrm{n} ( \mathrm{S} ) }$

When a coin toss there is only two possibilities = { H }  ,  { T } , So

n ( S ) = 2

And

n ( E ) =  1 for T  , So 

Getting tails in single toss   = $\frac{\mathbf{1}}{\mathbf{2}}$

And if coin tossed twice then total number of possibilities = { H , H }  ,  { H , T }, { T , H } and { T , T } , So

n ( S ) = 4

And

n ( E ) =  1 for { T , T }  , So 

Getting 2 tails in two tosses   = $\frac{\mathbf{1}}{\mathbf{4}}$

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