Question

A card is drawn at a random from a well-shuffled deck of playing cards. The probability that the card drawn is an ace or a red card is . NextReset

Answer 1

Answer:

$\frac{7}{13}$

Step-by-step explanation:

Total number of cards in deck of playing cards = 52

Number of ace in deck of playing cards i.e n(P)= 4

Number of red cards in deck of playing cards i,e n(Q) =

Number of diamonds + Number of hearts = 13+ 13 = 26

Number of ace which are red cards i,e $n(P\cap Q)$= 2

To Find: $n\left ( P\cup Q \right )$

Solution:

$n\left ( P\cup Q \right )=n\left ( P \right )+n\left ( Q \right )-n\left ( P\cap Q \right )\\=4+26-2\\=28$

So, probability that the card drawn is an ace or a red card = $n\left ( P\cup Q \right )$/Total number of cards

=$\frac{28}{52}=\frac{7}{13}$

Answer 2

P(Ace) = (4/52) =1/13
P(RED) = 1/2

P(ACE ∪ Red) = 1/13+ 1/2 = 15/26 = 0.577