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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.
Given:
A box contains cards numbered \( 3,5,7,9, .., 35,37 \).
A card is drawn at random from the box.
To do:
We have to find the probability that the number on the drawn card is a prime number.
Solution:
A box contains cards numbered \( 3,5,7,9, .., 35,37 \).
This implies,
The total number of possible outcomes $n=18$.
Prime numbers from 3 to 37 are $3, 5, 7, 11, 13, 17, 19, 23, 29, 31$ and $37$.
Total number of favourable outcomes $=11$.
We know that,
Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
Therefore,
Probability that the number on the drawn card is a prime number $=\frac{11}{35}$
$=\frac{11}{18}$
The probability that the number on the drawn card is a prime number is $\frac{11}{18}$.
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