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 $\frac{5}{24}$.       

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Updated on: 10-Oct-2022

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