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Random experiment – picking 2 pictures at random from a set of 10 pictures.
Therefore, sample space = 10C2 = 45.

Event – the two pictures are the ones that Jim hasn’t already bought
Therefore, favourable outcomes = 7C2 = 21

Required probability = Favourable outcomes / Sample Space = \(\frac{21 }{ 45}\) = \(\frac{7}{15}\).

The backdoor approach to solving this question is to subtract the events where the 2 pictures selected to consist of pictures already bought by Jim.

There can be two such cases:
Both the pictures were the ones already bought by Jim, which can be done in 3C2 ways i.e. 3 ways.
One of the pictures was the one already bought by Jim and the other was one which wasn’t; this can be done in 3C1 * 7C1 ways i.e. 3*7 = 21 ways.

Therefore, required probability = 1 – \(\frac{(3 + 21) }{ 45 }\)= 1 – \(\frac{24 }{ 45}\) = \(\frac{21 }{ 45}\) = \(\frac{7 }{ 15}\).

The correct answer option is D.

Hope that helps!
Aravind B T
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