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

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

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

Answer 2

`(7)/(13)`

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

=
`(28)/(52)=(7)/(13)`