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

Probability that withdrawn card is a club or a jack is
`(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A = event that the withdrawn card is club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B = event that the withdrawn card is jack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)=(|A|)/(|S|)=(13)/(52)\\\\P(B)=(|B|)/(|S|)=(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Probability that withdrawn card is a club or a jack is,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)=(|A\ \cap\ B|)/(|S|)=(1)/(52)`

Putting this,

`P(A\ \cup\ B)=(13)/(52)+(4)/(52)-(1)/(52)=(13+4-1)/(52)=(16)/(52)=(4)/(13)`