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 $(\frac{3}{26} )$

The probability of NOT picking a red face card from the deck  is $(\frac{23}{26} )$

Step-by-step 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)  = $\frac{\textrm{The number of red face cards}}{\textrm{Total number of cards}} = (\frac{6}{52} ) = (\frac{3}{26})$

Hence, the probability of picking a red face card from the deck  is $(\frac{3}{26} )$

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)

$= 1 - (\frac{3}{26} ) = \frac{26-3}{26} = (\frac{23}{26})$

Hence,  the probability of NOT picking a red face card from the deck  is $(\frac{23}{26} )$