Question

One card is randomly selected from a deck of cards. Find the odds against drawing a spade greater than 2 and less than 7.

Answer 1

The number of cards in a deck without jokers is 52. If you draw just one card then the probability is going to have 52 in the denominator

the cards between 2 and 7 in the spade suit are 3 4 5 6. Since you have written "between", 4 cards will be successful.

The answer is P(3,4,5,6) = 4/52 which reduces to 1/13

Answer 1/13.

Answer 2

The probability of an event happening is the number of ways it can happen divided by the number of outcomes. In this case, there are 52 outcomes (since there are 52 different possible cards you can pick). You now have to figure out how many ways this can happen (how many cards fit the requirements). There are 4 cards that would work: the 3 of spades, the 4 of spades, the 5 of spades, and the 6 of spades. So, you have:

4 possible ways / 52 possible outcomes,

meaning the probability is

4/52

Dividing the numerator and denominator by 4, this can be simplified to

$\frac{1}{13}$