MATH SOLVE

3 months ago

Q:
# 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')

Accepted Solution

A:

Answer:Hence, the probability is: 0.8846Step-by-step 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 Dand F' denote the complement of event F.Hence, we have:[tex]P(D'\bigcup F')=(P(D\bigcap F))'\\\\i.e.\\\\P(D'\bigcup F')=1-P(D\bigcap F)[/tex]D∩F denote the event that the card is a red card and is a face card as wellSince there are 6 cards which are face as well as red cards out of a total of 52 cards.Hence, we get:[tex]P(D'\bigcup F')=1-\dfrac{6}{52}\\\\i.e.\\\\P(D'\bigcup F')=\dfrac{52-6}{52}\\\\i.e.\\\\P(D'\bigcup F')=\dfrac{46}{52}\\\\P(D'\bigcup F')=0.8846[/tex]