A card is picked from a standard deck of 52 cards. Determine the odds against and the odds in favor of selecting a black card.
To determine the odds against and the odds in favor of selecting a black card from a standard deck of 52 cards, we first need to calculate the total number of favorable outcomes (black cards) and the total number of possible outcomes (all cards in the deck).
Step 1: Calculate the number of favorable outcomes (black cards)
A standard deck of 52 cards contains 26 black cards (clubs and spades).
Step 2: Calculate the number of possible outcomes (all cards in the deck)
A standard deck of 52 cards contains a total of 52 cards.
Step 3: Calculate the odds against
Odds against = (Number of unfavorable outcomes) / (Number of favorable outcomes)
In this case, the number of unfavorable outcomes is the number of non-black cards, which is 52 - 26 = 26.
So, the odds against selecting a black card are 26/26 = 1 (since the numerator and denominator are the same).
Step 4: Calculate the odds in favor
Odds in favor = (Number of favorable outcomes) / (Number of unfavorable outcomes)
In this case, the number of favorable outcomes is 26 (black cards), and the number of unfavorable outcomes is also 26 (non-black cards).
So, the odds in favor of selecting a black card are 26/26 = 1 (since the numerator and denominator are the same).
Therefore, both the odds against (1) and the odds in favor (1) of selecting a black card are equal.
To determine the odds against selecting a black card, we first need to find the number of favorable outcomes (selecting a card that is not black) and the number of unfavorable outcomes (selecting a black card).
There are 26 black cards in a standard deck (13 spades and 13 clubs). Since there are 52 cards in total, the number of favorable outcomes is 26.
The number of unfavorable outcomes can be found by subtracting the favorable outcomes from the total number of outcomes. So, the number of unfavorable outcomes is 52 - 26 = 26.
The odds against selecting a black card can be expressed as a ratio of unfavorable outcomes to favorable outcomes. In this case, the ratio is 26:26, which simplifies to 1:1.
Therefore, the odds against selecting a black card are 1 to 1.
To determine the odds in favor of selecting a black card, we simply reverse the ratio. So, the odds in favor of selecting a black card are also 1 to 1.
This is just like your number cube problem.
How many black cards?
How many non-black (red) cards?
odds in favor ... #black : #red
odds against ... the other way