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?

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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

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Answer 1 · 2018-03-16T15:47:01

$(\frac{32}{52})$ $(32/52)$

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)= $(\frac{26}{52})$ $(26/52)$

P(picture)= $(\frac{12}{52})$ $(12/52)$

For combined events, we use the formula:
P $(A \cup B)$ $(A uu B)$ = $P (A)$ $P(A)$ + $P (B)$ $P(B)$ - $P (A \cap B)$ $P(A nn B)$

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

P(picture or red)= $(\frac{26}{52}) + (\frac{12}{52}) - (\frac{6}{52})$ $(26/52)+(12/52)-(6/52)$

P(picture or red)= $(\frac{32}{52})$ $(32/52)$

Answer 2 · 2018-03-16T15:48:13

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 = $\frac{32}{52} = \frac{8}{13} \approx 0.6154$ $32/52 =8/13 \approx 0.6154$

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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?