Question

One card is randomly drawn from a deck of 52 cards. What is the probability of getting a jack or a spade?

Answer 1

P(jack or spade) = 4/13

Step-by-step explanation

There are 4 jacks in a deck of 52 cards, one for each suit, so the probability of drawing a jack is,

`P(jack)=(4)/(52)`

Each suit has 13 cards, so there are 13 spades in the 52-card deck. The probability of drawing a spade is,

`P(spade)=(13)/(52)`

There is only one jack of spades, so the probability of drawing that particular card is,

`P(jack.of.spades)=(1)/(52)`

The probability of drawing a jack or a spade is the probability of the union of the events where a jack is drawn or a spade is drawn,

`P(jack.or.spade)=P(jack\cup spade)`

And this is, by definition,

`P(jack\cup spade)=P(jack)+P(spade)-P(jack\cap spade)`

The probability of the intersection of the events is the probability that the card drawn is a jack of spades,

`P(jack\cup spade)=(4)/(52)+(13)/(52)-(1)/(52)=(4+13-1)/(52)=(16)/(52)=(4)/(13)`

Hence, P(jack or spade) = 4/13.