3cards are drawn from a standard deck of 52 cards. find the probability of drawing either 3 red cards or 3 face cards.

The probability of drawing either 3 red cards or 3 face cards is: 0.1267

Step-by-step explanation:

We are given a deck of 52 playing cards out of which we draw 3 cards.

We are asked to find the probability that the 3 card drawn are either 3 red cards or 3 face cards.

We know that in a playing cards we have 26 red cards and 12 face cards.

so we have to choose our card either from 26 red cards or 12 face cards and there are 6 cards which are both red card and is a face as well.

Let P denote the probability of an event.

Let A be the set that the card drawn is red.

B denote the set that the card drawn is a face card.

A∩B denote the set that the card drawn is red as well as is a face card.

We need to find the probability that the card drawn is either 3 red cards or 3 face cards i.e. we are asked to find P(A∪B)

We know that

P(A∪B)=P(A)+P(B)-P(A∩B)

Now  

Hence,

Hence, the probability of drawing either 3 red cards or 3 face cards is: 0.1267

x/3-10=8

x/3=18

x=48