Cards marked with numbers $11,12,13,\dots ,60$ are placed in a box and mixed thoroughly. One card is drawn at random from the box. Find the probability that the number on the drawn card is a perfect square.

Step-by-step solution

1. Determine total outcomes: the numbers are from $11$ to $60$ inclusive, so $n(S)=60-11+1=50$.
2. Identify the perfect squares between $11$ and $60$: $16=4^2$, $25=5^2$, $36=6^2$, and $49=7^2$.
3. Count the favorable outcomes: there are $4$ such numbers, so $n(E)=4$.
4. Calculate the probability: $P(E)=\frac{4}{50}=\frac{2}{25}$.

Concept tested: Probability with number cards

Published 24 August 2026 · How this solution was prepared and checked

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