Question

A single card is drawn form a standard 52 card deck. Let D be the event that the card drawn is red., and let F be the event that the card drawn is a face card. Find the indicated probabilities 1. P (D' U F')

Answer 1

Hence, the probability is:

0.8846

Explanation:

D be the event that the card drawn is red.

and F denote the event that the card drawn is a face card.

We are asked to find:

P(D'∪F')

We know that D' denote the complement of event D

and F' denote the complement of event F.

Hence, we have:

`P(D'\bigcup F')=(P(D\bigcap F))'\\\\i.e.\\\\P(D'\bigcup F')=1-P(D\bigcap F)`

D∩F denote the event that the card is a red card and is a face card as well

Since there are 6 cards which are face as well as red cards out of a total of 52 cards.

Hence, we get:

`P(D'\bigcup F')=1-(6)/(52)\\\\i.e.\\\\P(D'\bigcup F')=(52-6)/(52)\\\\i.e.\\\\P(D'\bigcup F')=(46)/(52)\\\\P(D'\bigcup F')=0.8846`