Question

A box contains $20$ cards, numbered from $1$ to $20$. A card is drawn from the box at random. Find the probability that the number on the drawn card is even, prime, and a multiple of $3.$

Answer 1

Step 1: Use formula for probability

$\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$

It is given that, the box contains $20$ cards, numbered from $1$ to $20$.

Thus, the number of possible outcomes is $20$

Step 2: Finding the probability that the number on the drawn card is even:

The favorable outcomes of getting an even number will be $2,4,6,8,10,12,14,16,18,20$

The probability of getting an even number is

$$\begin{gathered} =\frac{10}{20} \\ =\frac{1}{2} \end{gathered}$$

Step 3: Finding the probability that the number on the drawn card is prime:

The favorable outcomes of getting a prime number will be $2,3,5,7,11,13,17,19$

The probability of getting a prime number will be,

$$\begin{gathered} =\frac{8}{20} \\ =\frac{2}{5} \end{gathered}$$

Step 4: Finding the probability that the number on the drawn card is a multiple of $3$:

The favorable outcomes of getting a multiple of three will be $3,6,9,12,15,18$

The probability of getting a multiple of $3.$ will be,

$$\begin{gathered} =\frac{6}{20} \\ =\frac{3}{10} \end{gathered}$$

Hence, the probability that the number on the drawn card is even is $\frac{1}{2}$, prime is $\frac{2}{5}$, and a multiple of $3$ is $\frac{3}{10}$