Question

What is the probability that a card picked at random from a 52-card deck of playing cards is a club or a jack?

Answer 1

There are 13 clubs in a deck. 13/52
There are 4 jacks in a deck, though 1 is a club so we don't count it. 3/52
13+3=16/52 simplified to 4/13

Answer 2

Answer-

Probability that withdrawn card is a club or a jack is $\dfrac{4}{13}$

Solution-

Let us assume that,

S = number of ways one card can be drawn

|S| = 52

A = event that the withdrawn card is club

|A| = 13

B = event that the withdrawn card is jack

|B| = 4

Hence,

$P(A)=\dfrac{|A|}{|S|}=\dfrac{13}{52}\\\\P(B)=\dfrac{|B|}{|S|}=\dfrac{4}{52}$

Probability that withdrawn card is a club or a jack is,

$P(A\ \cup\ B)=P(A)+P(B)+P(A\ \cap\ B)$

As there is only one jack with suit as club, so

$P(A\ \cap\ B)=\dfrac{|A\ \cap\ B|}{|S|}=\dfrac{1}{52}$

Putting this,

$P(A\ \cup\ B)=\dfrac{13}{52}+\dfrac{4}{52}-\dfrac{1}{52}=\dfrac{13+4-1}{52}=\dfrac{16}{52}=\dfrac{4}{13}$