Olivia has a deck of well-shuffled playing cards. What are the odds:
a) in favour of drawing a red face card?
b) against drawing a black card?
I assume that you count 12 face cards in a deck, of which 6 are red
Prob(red face card) = 6/52 = 3/26
prob(NOT red face card) = 33/26
odds in favour of red face card = (3/26) : (33/26) = 3 : 33 = 1 : 11
let me know what you did for b)
the answer for b is 1:1
yes
To determine the odds, we need to know the total number of possible outcomes and the number of favorable outcomes.
a) In favor of drawing a red face card:
First, let's determine the number of red face cards in a deck. A standard deck of 52 playing cards has 2 red face cards of each suit, which are the King and Queen (since both are considered face cards). So, there are a total of 2 red face cards in each of the 4 suits, giving us a total of 2 * 4 = 8 red face cards.
A standard deck of playing cards has 52 cards in total. Since you have a well-shuffled deck, each card has an equal probability of being drawn. Therefore, the total number of possible outcomes is 52.
The odds in favor of drawing a red face card would be the number of favorable outcomes (8) divided by the number of total outcomes (52). So, the odds are 8/52, which can be simplified to 2/13.
b) Against drawing a black card:
Since a standard deck has 52 cards, we need to determine the number of black cards. Black cards consist of clubs and spades, which are half of the suits in the deck. Each suit has 13 cards, so 2 suits (clubs and spades) give us a total of 13 * 2 = 26 black cards.
The odds against drawing a black card would be the number of unfavorable outcomes (26) divided by the number of total outcomes (52). So, the odds are 26/52, which can be simplified to 1/2.
Therefore, the odds are a) 2/13 in favor of drawing a red face card and b) 1/2 against drawing a black card.