Probability

Question

A card is drawn from a 52-card deck, and the events C & D are as follows: C= It is a jack D= It is a spade. Find the probability of event C or event D occurring, P(C U D).

Answer 1

First let's write down the formula:

 

P(C U D) = P(C) + P(D) - P(C ∩ D)

 

let's find each of these terms:

 

1) P(C) =?

 

  There are 52 cards, and 4 of them are jack. So clearly the probability of choosing a Jack would be:

 

  P(C) = 4/52 

 

2) P(D) =?

 

There are 52 cards, and 13 of them are spade. So clearly the probability of choosing a Jack would be:

 

P(D) = 13/52 

 

3)  P(C ∩ D)=?

 

  There are 52 cards, and only one card is both jack and spade (jack of spade). So:

 

P(C ∩ D)= 1/52

 

 

So: P(C U D) = (4/52) + (13/52) - (1/52) = 16/52 = 4/13