# A box contains cards numbered 3,5,7,9,……35,37. A card is drawn at random from the box. Find the probability that the number on the drawn card is a prime number.

Last updated date: 24th Mar 2023

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Answer

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Hint: Start with determining how many numbers are there in 3,5,7,9,……35,37 for total number of favorable outcomes. And also how many prime numbers it exhibits.

According to the question, the numbers on the cards represent 3,5,7,9,……35,37. It consists of all the odd numbers up to 37 except 1.

So, total number of cards $ = \dfrac{{37 - 3}}{2} + 1 = 17 + 1 = 18$

Therefore, the total number of possible outcomes $ = 18$

Now in these, the cards representing prime numbers will be of number 3,5,7,11,13,17,19,23,29,31,37. Thus, there are 18 of these cards.

Therefore the number of favorable outcomes $ = 11$.

Let $E$is the event representing the drawing of a prime numbered card. Then the probability is:

$

\Rightarrow P\left( E \right) = \dfrac{{{\text{No}}{\text{. of favorable outcomes}}}}{{{\text{Total number of possible outcomes}}}}, \\

\Rightarrow P\left( E \right) = \dfrac{{11}}{{18}}. \\

$

Thus, the required probability is $\dfrac{{11}}{{18}}$.

Note: Probability represents the chance of an event to occur. For example in above, the probability is $\dfrac{{11}}{{18}}$. This means that out of 18 trials of drawing the card, there is a chance that 11 of them comes out with a prime number.

According to the question, the numbers on the cards represent 3,5,7,9,……35,37. It consists of all the odd numbers up to 37 except 1.

So, total number of cards $ = \dfrac{{37 - 3}}{2} + 1 = 17 + 1 = 18$

Therefore, the total number of possible outcomes $ = 18$

Now in these, the cards representing prime numbers will be of number 3,5,7,11,13,17,19,23,29,31,37. Thus, there are 18 of these cards.

Therefore the number of favorable outcomes $ = 11$.

Let $E$is the event representing the drawing of a prime numbered card. Then the probability is:

$

\Rightarrow P\left( E \right) = \dfrac{{{\text{No}}{\text{. of favorable outcomes}}}}{{{\text{Total number of possible outcomes}}}}, \\

\Rightarrow P\left( E \right) = \dfrac{{11}}{{18}}. \\

$

Thus, the required probability is $\dfrac{{11}}{{18}}$.

Note: Probability represents the chance of an event to occur. For example in above, the probability is $\dfrac{{11}}{{18}}$. This means that out of 18 trials of drawing the card, there is a chance that 11 of them comes out with a prime number.

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