The complementary of any event $A$ is the event when $A$ does not occur or happen. Event \(

Question

The complementary of any event $A$ is the event when $A$ does not occur or happen. Event $A$ Complement of $A$, $A'$ Win a game of chessDon’t win a game of chess. (Note: Don’t win is not the same as losing a game as the game can end with a draw.) Taking the busNot taking the bus Rainy dayNot a rainy day Rolling a “6” on a dieNot rolling a “6” on a die The complement of $A$ is denoted by $A'$ or ${{A}^{c}}$, consists of all the outcomes in which the event $A$ does not occur. $\mathrm{P}\left( A' \right)=1-\mathrm{P}\left( A \right)$ In other words, $\mathrm{P}\left( \mathrm{not }A \right)=1-\mathrm{P}\left( A \right)$. A card is drawn at random from the 26 playing cards shown above. Find the probability of drawing a queen, not drawing a queen, an odd number, not an odd number. For the number questions, count each ace as 1; kings, queens and jacks have no numerical value.

Accepted Answer

(i) $\frac1{13}$ (ii) $\frac{12}{13}$ (iii) $\frac5{13}$ (iv) $\frac8{13}$

Complementary Events

Complementary Events

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Event \(A\)	Complement of \(A\), \(A'\)
Win a game of chess	Don’t win a game of chess. (Note: Don’t win is not the same as losing a game as the game can end with a draw.)
Taking the bus	Not taking the bus
Rainy day	Not a rainy day
Rolling a “6” on a die	Not rolling a “6” on a die