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Cards marked with number 3, 4, 5, ...., 50 are placed in a box and mixed thoroughly. A card is drawn at random form the box. Find the probability that the selected card bears a perfect square number. - Mathematics

Cards marked with number 3, 4, 5, ...., 50 are placed in a box and mixed thoroughly. A card is drawn at random form the box. Find the probability that the selected card bears a perfect square number.

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Solution

It is given that the box contains cards marked with numbers 3, 4, 5, ..., 50.

∴ Total number of outcomes = 48

Between the numbers 3 and 50, there are six perfect squares, i.e. 4, 9, 16, 25, 36 and 49.

∴ Number of favourable outcomes = 6

∴ Probability that a card drawn at random bears a perfect square = `"Number of favourable outcomes"/"Total number of outcomes"=6/48=1/8`

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