Question

One card is selected at random from a standard deck of cards of 52. what is the probablity that the card selected is red or picture card?

one card is selected at random from a standard deck of cards of 52. what is the probablity that the card selected is red or picture card

Answer 1

`(32/52)`

Explanation:

In a deck of cards, half of the cards are red (26) and (assuming no jokers) we have 4 jacks, 4 queens and 4 kings (12).

However, of the picture cards, 2 jacks, 2 queens, and 2 kings are red.
What we want to find is "the probability of drawing a red card OR a picture card"
Our relevant probabilities are that of drawing a red card or a picture card.

P(red)=`(26/52)`

P(picture)=`(12/52)`

For combined events, we use the formula:
P`(A uu B)`=`P(A)`+`P(B)`-`P(A nn B)`

Which translates to:
P(picture or red)=P(red)+P(picture)-P(red and picture)

P(picture or red)=`(26/52)+(12/52)-(6/52)`

P(picture or red)=`(32/52)`

Answer 2

Number of red cards = 26 (diamonds and hearts)

Number of picture cards = 3*4 = 12 (J,Q,K of each of the 4 suits)

Number of picture cards that are red = 3*2 = 6 (J,Q,K of diamonds and clubs)

Number of picture cards or red = (26 + 12 - 6) = 32

P(red or picture) = Number of favorable / Number of total = `32/52 =8/13 \approx 0.6154`