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Mathematics

Cards numbered 1 to 20 are placed in a box and mixed thoroughly. A card is drawn at random from the box. What is the probability that the card drawn bears a number which is a multiple of 3 or 5 or both?

  1. (12)\Big(\dfrac{1}{2}\Big)

  2. (25)\Big(\dfrac{2}{5}\Big)

  3. (815)\Big(\dfrac{8}{15}\Big)

  4. (920)\Big(\dfrac{9}{20}\Big)

Probability

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Answer

The cards are numbered from 1 to 20.

Total number of outcomes = 20

Let E be the event of getting a number multiple of 3 or 5, then

E = {3, 5, 6, 9, 10, 12, 15, 18, 20}

The number of favorable outcomes to the event E = 9

∴ P(E) = Number of favorable outcomesTotal number of outcomes=920\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{9}{20}

Hence, option 4 is the correct option.

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