Question

A card is picked from a standard deck of 52 cards. Determine the odds against and the odds in favor of selecting a red face card (king, queen, or jack ).

Answer 1

The probability of picking a red face card from the deck is
`((3)/(26) )`

The probability of NOT picking a red face card from the deck is
`((23)/(26) )`

Explanation:

The total number of cards in the deck = 52

The total number of red( Diamond + Hearts) face cards in the given deck

= 2 Red Queens + 2 Red jacks + 2 Red kings = 6 cards

Let E : Event of picking a red face card from the deck

Now , P( any event) =
`\frac{\textrm{The number of favorable observations}}{\textrm{Total number of observations}}`

So, here P(Picking a red face card) =
`\frac{\textrm{The number of red face cards}}{\textrm{Total number of cards}} = ((6)/(52) ) = ((3)/(26))`

Hence, the probability of picking a red face card from the deck is
`((3)/(26) )`

Now, as we know P (any event NOT A) = 1 - P(any event A)

So, P(NOT Picking a red face card) = 1 - P(Picking a red face card)

`= 1 - ((3)/(26) ) = (26-3)/(26) = ((23)/(26))`

Hence, the probability of NOT picking a red face card from the deck is
`((23)/(26) )`