Question

The chance to fail in Physics is 20% and the chances to fail in mathematics are 10%.What are the chances to fail in any of the subjects?
A.28%
B.38%
C.72%
D.82%

Answer 1

We are given the probability of two events and we are asked to find the probability of the union of the events which is given by the formula $P(A \cup B) = P(A) + P(B) - P(A \cap B)$and as the events are independent we have $P(A \cap B) = P(A).P(B)$and substituting the given values we obtain the required answer

Complete step-by-step answer:
We are given that the probability to fail in physics is 20% and the probability to fail in mathematics is 10%
Let A be the event of failing in physics
Let B be the event of failing in mathematics
We are given
$\Rightarrow P(A) = \dfrac{{20}}{{100}} = \dfrac{1}{5} \\\ \Rightarrow P(B) = \dfrac{{10}}{{100}} = \dfrac{1}{{10}} \\\$
We are asked to find the probability of failing in any one of the subjects ,
That is, either physics or mathematics
So we need to find the probability of the union of the events A and B, which is given by
$\Rightarrow P(A \cup B) = P(A) + P(B) - P(A \cap B)$
Since the events are independent $P(A \cap B) = P(A).P(B)$
Substituting the values we get,
$\Rightarrow P(A \cup B) = \dfrac{1}{5} + \dfrac{1}{{10}} - \dfrac{1}{5}\dfrac{1}{{10}} = \dfrac{1}{5} + \dfrac{1}{{10}} - \dfrac{1}{{50}}$
Taking LCM we get
$\Rightarrow P(A \cup B) = \dfrac{{10 + 5 - 1}}{{50}} = \dfrac{{14}}{{50}}$
We are asked for the percentage so lets multiply and divide by 2
$\Rightarrow \dfrac{{14}}{{50}}*\dfrac{2}{2} = \dfrac{{28}}{{100}} = 28\%$
Therefore the probability of failing in any one subject is 28%
The correct option is A.

Note: A probability of 0 means that an event is impossible.
A probability of 1 means that an event is certain.
An event with a higher probability is more likely to occur
Probabilities are always between 0 and 1.
The probabilities of our different outcomes must sum to 1.