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Question

A box contains $$25$$ cards numbered from $$1$$ to $$25$$. A card is drawn at random from the bad. Find the probability that the number on the drawn card is divisible by $$2$$ or $$3$$.


Solution

Total numbers of cards $$=25$$

The favourable outcome = numbers divisible by $$2=\left\{ 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24\right\}$$
The favourable outcome = number divisible by $$3=\left\{ 3, 6, 9, 12, 15, 18, 21, 24 \right\}$$
Total number of favorable outcomes $$=16$$
( Note: count $$6, 12, 18$$ and $$24$$ are common, so consider only one set )

Probability is given by,
$$\displaystyle P(A)$$$$=\dfrac{\text{no. of possible outcomes}}{\text{No. of total outcomes}}$$

Now, $$P($$ drawn card is divisible by $$2$$ or $$3)=16/25$$

Mathematics
RS Agarwal
Standard X

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