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Question

Two coins are tossed simultaneously. Find the probability that either exactly two heads or atleast one tail turn up

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Solution

Sample space S={HH,HT,TH,TT}n(S)=4
Let, A be the event of getting exactly two heads.
Then A={HH} and n(A)=1P(A)=n(A)n(S)=14
Let, B be the event of getting atleast one tail.
Then B={HT,TH,TT} and n(B)=3
P(B)=n(B)n(S)=34
Now, the events A and B are mutually exclusive.
P(AB)=P(A)+P(B)( addition rule of probability)
P(AB)=14+34=1
the probability of getting exactly two heads or at least one tail is 1.

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