Two students Anil and Ashima appeared in an examination. The probability that Anil will qualify the examination is $0.05$ and that Ashima will qualify the examination is $0.10 .$ The probability that both will qualify the examination is $0.02 .$ Find the probability that Only one of them will qualify the examination.

Vedclass pdf generator app on play store
Vedclass iOS app on app store

Let $E$ and $F$ denote the events that Anil and Ashima will qualify the examination, respectively. Given that

$P(E)=0.05$,  $P(F)=0.10$ and $P(E \cap F)=0.02$

Then

The event only one of them will qualify the examination is same as the event either (Anil will qualify, andAshima will not qualify) or (Anil will not qualify and Ashima will qualify) i.e., $E \cap F ^{\prime}$ or $E ^{\prime} \cap F ,$ where $E \cap F ^{\prime}$ and $E ^{\prime} \cap F$ are mutually exclusive.

Therefore, $P$ (only one of them will qualify) $=P(E \cap F^{\prime} $ or $E^{\prime} \cap F)$

$= P \left( E \cap F ^{\prime}\right)$ $+ P \left( E ^{\prime} \cap F \right)$ $= P ( E )- P ( E \cap F )+ P ( F )- P ( E \cap F ) $

$=0.05-0.02+0.10-0.02=0.11$

Similar Questions

If $E$ and $F$ are events such that $P ( E )=\frac{1}{4}$, $P ( F )=\frac{1}{2}$ and $P(E$ and $F )=\frac{1}{8},$ find : $P ( E$ or  $F )$

One card is drawn from a pack of $52$ cards. The probability that it is a queen or heart is

If $A$ and $B$ are any two events, then $P(\bar A \cap B) = $

The probability that a man will be alive in $20$ years is $\frac{3}{5}$ and the probability that his wife will be alive in $20$ years is $\frac{2}{3}$. Then the probability that at least one will be alive in $20$ years, is

If an integer is chosen at random from first $100$ positive integers, then the probability that the chosen number is a multiple of $4$ or $6$, is