In a lottery of 50 tickets numbered 1 to 50, one ticket is drawn. Find the probability that the drawn ticket bears a prime number.
Given:
In a lottery of 50 tickets numbered 1 to 50, one ticket is drawn.
To do:
We have to find the probability that the drawn ticket bears a prime number.
Solution:
Total number of tickets $=50$
This implies,
The total number of possible outcomes $n=50$.
Prime numbers from 1 to 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47.
Number of tickets bearing a prime number $=15$
Total number of favourable outcomes $=15$.
We know that,
Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
Therefore,
Probability that the drawn ticket bears a prime number $=\frac{15}{50}$
$=\frac{3}{10}$
The probability that the drawn ticket bears a prime number is $\frac{3}{10}$.
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