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Cards numbered 1 to 30 are put in a bag. A card is drawn at random from this bag. Find the probability that the number on the drawn card is a prime number great than 7.
Given:
Cards numbered 1 to 30 are put in a bag. A card is drawn at random from this bag.
To do:
We have to find the probability that the number on the drawn card is a prime number great than 7.
Solution:
Total number of cards $=30$
This implies,
The total number of possible outcomes $n=30$.
Prime numbers greater than 7 from 1 to 30 are 11, 13, 17, 19, 23 and 29.
Total number of prime numbers greater than 7 from 1 to 30 $=6$
Total number of favourable outcomes $=6$.
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 great than 7 $=\frac{6}{30}$
$=\frac{1}{5}$
The probability that the number on the drawn card is a prime number greater than 7 is $\frac{1}{5}$.