Question & Answer
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.

ANSWER Verified Verified
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.

Complete step-by-step answer:
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 \[=\dfrac{Favorable\ outcomes}{Total\ outcomes}\].