Question

One card is randomly selected from a deck of cards. Find the odds against drawing an eight The odds against drawing an eight are (Simplify your answers.)

Answer 1

Answer:

The odds against drawing an eight are $\frac{12}{13}$

Step-by-step explanation:

If there are 52 cards in a deck, 13 cards a suit and 4 suits, that means there are four eights in the deck, one of every suit.

That means, the probability of drawing an eight is:

$P_{eight}=\frac{number of eights}{cards} =\frac{4}{52}=\frac{1}{13}$

As we want to find the odds against drawing an eight, we want to find the probability of not drawing an eight.

The probability of drawing or not drawing an eight is one (the probability of taking a card if we take a card), and as they are not independent, we know that we have to sum those probabilities:

$P_{card} =P_{eight}+P_{not eight}= 1$

Then, we can find the probability of not drawing an eight:

$P_{not eight}= 1- P_{eight}=1-\frac{1}{13} =\frac{12}{13}$

That means, in average, 12 out of 13 times we will not draw an eight.