Question

One card is drawn at random from a well-shuffled deck of 52 cards. Find the probability that the card drawn is (i) a king, (ii) not a king.

Hint:

In probability, remember \( P(\text{not event}) = 1 - P(\text{event}) \). For a standard deck, there are 4 cards of each rank.

Answer 1

Step 1: Total number of possible outcomes.
In a standard deck of 52 playing cards, \[ \text{Total number of outcomes} = 52 \]
Step 2: Number of favourable outcomes for a king.
There are 4 kings in a deck (one from each suit: hearts, diamonds, clubs, spades). \[ \text{Favourable outcomes for a king} = 4 \]
Step 3: Probability of drawing a king.
\[ P(\text{king}) = \frac{\text{Favourable outcomes}}{\text{Total outcomes}} = \frac{4}{52} = \frac{1}{13} \]
Step 4: Probability of not drawing a king.
\[ P(\text{not a king}) = 1 - P(\text{king}) = 1 - \frac{1}{13} = \frac{12}{13} \] Step 5: Final Answers.
\[ \boxed{P(\text{king}) = \frac{1}{13}, \quad P(\text{not a king}) = \frac{12}{13}} \]