Probability

A student of mine came up with this question
Q:A coin is thrown twice, The sample space S is(HH,HT,TT). if A=(HH,TT) B=(HT,TT) what is the probability of .

i.A
ii. B
iii.AB
iv. A+B


Solution
if i got you right


Note the sample space is the total outcome  is 6
our Sample space=6

Probability of A?
events in A is 4 ie Head, Head, Tail,Tail
Pr(A)=4/6
=2/3


Probability of B?
events in B ie Head, Tail,Tail,Tail =4
Pr(B) = 4/6
=2/3

Probability AB?
=(2/3*2/3)
4/9

Pr (A+B)
=(2/3+2/3)
=4/3

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