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Explanation:

Each bag has a2 – 6a + 10 balls.

Bags 1, 2, 3 and 4 contain 1, 3, 5 and 7 black balls respectively.

Probability of selecting a black ball from a specific bag is

na2-6a+9

where n is the number of black balls in that bag.

A bag is selected at random.

∴ Probability of selecting a particular bag = 14

∴ Probability that the ball selected from that randomly chosen bag is black

141a2-6a+10 + 143a2-6a+10 + 145a2-6a+10 + 147a2-6a+10

=1416a2-6a+10 = 4a2-6a+10

Hence, option (d).

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