Question

$AandB$ play a game where each is asked to select a number from $1to25.$ If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial is

• A. $\frac{1}{25}$
• B. $\frac{24}{25}$
• C. $\frac{2}{25}$
• D. None of these

Answer 1

The correct option is B

$\frac{24}{25}$

Explanation for the correct options:

Probability:

$$\begin{gathered} \text{Total number of cases}=25\times 25 \\ \text{Favourable cases}=25 \end{gathered}$$

The probability of winning a prize

$$\begin{gathered} =\frac{25}{25\times 25} \\ =\frac{1}{25} \end{gathered}$$

Hence, the probability of not winning prize

$$\begin{gathered} =1-\frac{1}{25} \\ =\frac{24}{25} \end{gathered}$$

Hence, option(B) is correct .