Let $A, B, C$ be three mutually independent events. Consider the two statements ${S_1}$ and ${S_2}$
${S_1}\,\,:\,\,A$ and $B \cup C$ are independent
${S_2}\,\,:\,\,A$ and $B \cap C$ are independent
Then
In each of the following experiments specify appropriate sample space A person is noting down the number of accidents along a busy highway during a year.
A card is selected from a pack of $52$ cards. Calculate the probability that the card is an ace of spades.
If $\frac{2}{11}$ is the probability of an event, what is the probability of the event $'$ not $A ^{\prime}$.
Three letters are dictated to three persons and an envelope is addressed to each of them, the letters are inserted into the envelopes at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope.