If $A$ and $B$ are any two events, then the probability that exactly one of them occur is
$P\,(A) + P\,(B) - P\,(A \cap B)$
$P\,(A) + P\,(B) - 2P\,(A \cap B)$
$P\,(A) + P\,(B) - P\,(A \cup B)$
$P\,(A) + P\,(B) - 2P\,(A \cup B)$
In a class of $125$ students $70$ passed in Mathematics, $55$ in Statistics and $30$ in both. The probability that a student selected at random from the class has passed in only one subject is
If $A$ and $B$ are arbitrary events, then
A die is thrown. Let $A$ be the event that the number obtained is greater than $3.$ Let $B$ be the event that the number obtained is less than $5.$ Then $P\left( {A \cup B} \right)$ is
Check whether the following probabilities $P(A)$ and $P(B)$ are consistently defined $P ( A )=0.5$, $ P ( B )=0.7$, $P ( A \cap B )=0.6$
An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on the is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cards numbered $1, 2, 3,….., 9$ is randomly picked and the number on the card is noted. The probability that the noted number is either $7$ or $8$ is