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Cards marked with numbers \( 13,14,15, \ldots, 60 \) are placed in a box and mixed thoroughly. One card is drawn at random from the box. Find the probability that number on the card drawn is divisible by 5.
Given:
Cards marked with numbers \( 13,14,15, \ldots, 60 \) are placed in a box and mixed thoroughly. One card is drawn at random from the box.
To do:
We have to find the probability that the number on the card drawn is divisible by 5.
Solution:
Cards marked with numbers \( 13,14,15, \ldots, 60 \) are placed in a box.
This implies,
The total number of possible outcomes $n=48$.
Numbers divisible by 5 from 13 to 60 are $15, 20, 25, 30, 35, 40, 45, 50, 55$ and $60$.
Total number of favourable outcomes $=10$.
We know that,
Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
Therefore,
Probability that the number on the card drawn is divisible by 5 $=\frac{10}{48}$
$=\frac{5}{24}$
The probability that the number on the card drawn is divisible by 5 is $\frac{5}{24}$.