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?

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Answer 1 · 2016-10-22T08:04:51

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

If we denote the events as:

$A$ $A$ - a jack is chosen and

$B$ $B$ - a spade is chosen

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

The probability can be calculated using the formula:

$P (A \cup B) = P (A) + P (B) - P (A \cap B)$ $P(AuuB)=P(A)+P(B)-P(AnnB)$

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

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

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

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

Finally if we substitute calculated values we get:

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

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

So the answer can be written as:

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