# A card is drawn at random from a well-shuffled deck of 52 cards.

Question:

A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of its being a spade or a king.

Solution:

let A denote the event that the card drawn is spade and B denote the event that card drawn is king.

In a pack of 52 cards, there are 13 spade cards and 4 king cards

Given : $P(A)=\frac{13}{52}, P(B)=\frac{4}{52}$

To find : Probability that card drawn is either a queen or heart $=P(A$ or $B)$

The formula used : Probability =

$P(A$ or $B)=P(A)+P(B)-P(A$ and $B)$

$P(A)=\frac{13}{52}$ (as favourable number of outcomes $=13$ and the total number of outcomes = 52)

$P(B)=\frac{4}{52}$ (as favourable number of outcomes $=4$ and the total number of outcomes = 52)

The probability that card is drawn is both spade and king = P(A and B)= 1

(as there is one card which is both spade and king i.e. king of spades)

$P(A$ or $B)=\frac{13}{52}+\frac{4}{52}-1$

$\mathrm{P}(\mathrm{A}$ or $\mathrm{B})=\frac{13+4-1}{52}=\frac{16}{52}=\frac{4}{13}$

$P(A$ or $B)=\frac{4}{13}$

Probability of a card drawn is either a spade or king $=P(A$ or $B)=\frac{4}{13}$