QUESTION

# A box contains cards numbered from 1 to 50. One card is drawn at random from the box. Find the probability that the number on the card is(a) a perfect square.(b) a number divisible by 6.

Hint: The formula for evaluating probability of any event is
P $=\dfrac{Favorable\ outcomes}{Total\ outcomes}$.
Another important thing which is useful for this question is that drawing a card from the box at random is nothing but taking out a card without having biased towards any card and without having any prior information regarding the cards.

Now, in the question it is mentioned that there are 50 cards numbered from 1 to 50. So, the total outcomes for the event of drawing a card from the box at random is
Total outcomes $=50$
Now, for the favorable outcomes for part (a) that is getting a card with a number which is a perfect square, we need to count the total number of cards that have a number which is a perfect square.
Therefore,
Favorable outcomes $=7$.
(1, 4, 9, 16, 25, 36, 49)
Now, using the formula for calculating the probability of getting a card numbered with a perfect square is
\begin{align} & =\dfrac{Favorable\ outcomes}{Total\ outcomes} \\ & =\dfrac{7}{50} \\ \end{align}
Hence, the probability of getting a card numbered with a perfect square is $\dfrac{7}{50}$.
Similarly, for part (b) that is for finding the probability of getting a card from the box that has a number which is divisible by 6, the favorable outcomes are
$=6$.
(6, 12, 18, 24, 30, 36)
Now, using the formula for calculating the probability of getting a card from the box that has a number which is divisible by 6, we get
\begin{align} & =\dfrac{Favorable\ outcomes}{Total\ outcomes} \\ & =\dfrac{6}{50} \\ & =\dfrac{3}{25} \\ \end{align}
Hence, the probability of getting a card numbered with a number that is divisible by 6 is $\dfrac{3}{25}$.

Note: The students can make an error if they don’t have any information about the formula for calculating the probability about any event which is given in the hint as
P $=\dfrac{Favorable\ outcomes}{Total\ outcomes}$.