If $A$ and $B$ are any two events, then the probability that exactly one of them occur is
$P\,(A) + P\,(B) - P\,(A \cap B)$
$P\,(A) + P\,(B) - 2P\,(A \cap B)$
$P\,(A) + P\,(B) - P\,(A \cup B)$
$P\,(A) + P\,(B) - 2P\,(A \cup B)$
Two dice are thrown simultaneously. The probability that sum is odd or less than $7$ or both, is
If $P(A)=\frac{3}{5}$ and $P(B)=\frac{1}{5},$ find $P(A \cap B)$ if $A$ and $B$ are independent events
If ${A_1},\,{A_2},...{A_n}$ are any $n$ events, then
Fill in the blanks in following table :
$P(A)$ | $P(B)$ | $P(A \cap B)$ | $P (A \cup B)$ |
$0.35$ | ........... | $0.25$ | $0.6$ |
In a class of $60$ students, $30$ opted for $NCC$ , $32$ opted for $NSS$ and $24$ opted for both $NCC$ and $NSS$. If one of these students is selected at random, find the probability that The student has opted $NSS$ but not $NCC$.