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A box contains 15 marbles out of which 7 are red and the rest are blue. Another box contains 14 marbles out of which 8 are blue and the rest are red. One marble is drawn from each box without replacement. Find the probability that each marble is of a different colour.

A box contains 15 marbles out of which 7 are red and the rest are blue. Another box contains 14 marbles out of which 8 are blue and the rest are red. One marble is drawn from each box without replacement. Find the probability that each marble is of a different colour. Correct Answer 52/105

Given:

A box contains 15 marbles out of which 7 are red and the rest are blue. Another box contains 14 marbles out of which 8 are blue and the rest are red. One marble is drawn from each box.

Formula:

The probability of drawing out a red ball from a set of (x + y) balls which has x red balls = x/(x + y)

Calculation:

⇒ Box A = 7 red and 8 blue

⇒ Box B = 8 blue and 6 red

Case 1:

⇒ Red from A and blue from B = 7/15 × 8/14 = 4/15

Case 2:

⇒ Blue from A and red from B = 8/15 × 6/14 = 8/35

⇒ Total = 4/15 + 8/35 = 52/105

∴ Required probability = 52/105

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