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
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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 donâ€™t have any information about the formula for calculating the probability about any event which is given in the hint as P \[=\dfrac{Favorable\ outcomes}{Total\ outcomes}\].