For the experiment of tossing a coin three times, how do you find the probability of getting at least one head?

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Answer 1 · 2017-04-26T17:56:08

#7/8.#

The Sample Space #S,# associated with the Experiment of

tossing a coin thrice is,

#S={(H,H,H),(H,H,T),(H,T,H),(H,T,T),(T,H,H),(T,H,T),(T,T,H),(T,T,T)}.#

#:. n(S)=8.#

#E=#the Event getting at least one Head

#=#the Event getting no. of Heads 1, or, 2, or 3

#:. E={(H,H,H),(H,H,T),(H,T,H),(H,T,T),(T,H,H),(T,H,T),(T,T,H)}.#

#:. n(E)=7.#

#:. P(E)=(n(E))/(n(S))=7/8.#

As an Aliter, we note that,

#E'=#the Complementary Event of the Event E

#=#the Event getting not a single Head at all

#:. E'={(T,T,T)} rArr P(E')=1/8.#

#:. P(E)=1-P(E')=1-1/8=7/8.#

Enjoy Maths.!