# A card is drawn from a standard deck of 52 playing cards. How do you find the probability that the card is a jack or a spade. Express the probability as a simplified fraction?

Oct 22, 2016

The probability is $\frac{4}{13}$

#### Explanation:

If we denote the events as:

$A$- a jack is chosen and

$B$ - a spade is chosen

Then the evemt we are looking for can be described as the alternative A or B ($A \cup B$).

The probability can be calculated using the formula:

$P \left(A \cup B\right) = P \left(A\right) + P \left(B\right) - P \left(A \cap B\right)$

Now we have to calculate the probabilities on the right side:

$P \left(A\right) = \frac{4}{52}$ because there are $4$ jacks in a deck of cards

$P \left(B\right) = \frac{13}{52}$ because there are $13$ spades

$P \left(A \cap B\right) = \frac{1}{52}$ because there is one card which is jack and a spade (a jack of spades).

Finally if we substitute calculated values we get:

$P \left(A \cup B\right) = \frac{4}{52} + \frac{13}{52} - \frac{1}{52} = \frac{16}{52}$

This result can be simplified because both numerator and denominator can be divided by $4$.

So the answer can be written as:

The probability is $\frac{4}{13}$