Question

The chances to fail in Physics are $20\%$ and the chances to fail in Mathematics are $10\%$. What are the chances to fail in at least one subject?

• A. $28\%$
• B. $38\%$
• C. $72\%$
• D. $82\%$

Answer 1

The correct option is A

$28\%$

Explanation for the correct option:

Step 1: Finding the chances

Given, The chances to fail in Physics are $20\%$ and the chances to fail in Mathematics are $10\%$

Let, The chance of failing in physics be, $P\left(A\right)$ $=\frac{20}{100}=\frac{1}{5}=0.2$, and

Let The chance of failing in mathematics be, $P\left(B\right)$ $=\frac{10}{100}=\frac{1}{10}=0.1$

The events are independent of each other.

Step 2: Finding the chances to fail in at least one subject

Since the events are independent of each other, the formulae are as follows

The probability of not failing in at least one subject will be,

$\mathit{P}\mathbf{(}\mathit{A}\mathbf{\cup }\mathit{B}\mathbf{)}\mathbf{=}\mathit{P}\left(A\right)\mathbf{+}\mathit{P}\left(B\right)\mathbf{-}\mathit{P}\left(A\right)\mathbf{.}\mathit{P}\left(B\right)\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\left[\because P(A\cap B)=P\left(A\right)P\left(B\right)\right]$

$$\begin{gathered} =0.2+0.1-\left(0.2\times 0.1\right) \\ =0.3-0.02 \\ =0.28 \\ =28\% \end{gathered}$$

Hence, option (A) is the correct answer.