Question

Cards marked with numbers $3,4,5.......,50$ are placed in a box and mixed thoroughly. A card is drawn at random from the box. Find the probability that the selected card bears a perfect square number.
A. $\dfrac{1}{2}$
B. $\dfrac{1}{4}$
C. $\dfrac{1}{6}$
D. $\dfrac{1}{8}$

Answer 1

Hint:Here first we will take squares of given numbers. We will take probability in between numbers. Then we will take probability for cards and we will use a formula for clearing this question. Then we will get a perfect square for the given number.

Complete step by step solution:It is given that the box contains marks with number $3,4,5......,50$.
So, the total number of outcomes is $48$.
Between the numbers $3$ and $50$, there are six perfect squares, $4,9,16,25,36$ and $49$.
$ \Rightarrow $ Number of favorable outcomes $ = 6$
$ \Rightarrow $ probability that a card drawn at random bears perfect square
We will use the formula for solving this question. That formula given below.
$ \Rightarrow $\[ \dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Total number of outcomes}}}}\]
$ \Rightarrow $\[ \dfrac{6}{{48}} \]
$ \Rightarrow $\[ \dfrac{1}{8} \]

So, the probability of given numbers square is $\dfrac{1}{8}$.

Additional information:
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes. How likely they are. The analysis of events governed by probability is called statistics. Probability is a branch of mathematics that deals with the occurrence of a random event. For example, when a coin is tossed in the air, the possible outcomes are Head and Tail.

Note: A little paradoxical, probability theory applies precise calculations to quantify uncertain measures of random events. In its simplest form, probability can be expressed mathematically as: the number of occurrences of a targeted event divided by the number of occurrences plus the number of failures of occurrences (this adds up to the total of possible outcomes).