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 #4/13#

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 (#AuuB#).

The probability can be calculated using the formula:

#P(AuuB)=P(A)+P(B)-P(AnnB)#

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

#P(A)=4/52# because there are #4# jacks in a deck of cards

#P(B)=13/52# because there are #13# spades

#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(AuuB)=4/52+13/52-1/52=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 #4/13#