What is the probability that the card is either an ace or heart?

Question

A single card is drawn from a standard 52-card deck. Calculate the probability and odds for the following event.

An ace or heart is drawn.

 

What is the probability that the card is either an ace or heart?

(Simplify answer in an integer or a fraction)

Answer 1

the probability that an ace is drawn is 4/52, or 1/13

the probability that a heart is drawn is 13/52, or 1/4

don't forget that one of the aces is the ace of hearts

P(an ace or heart is drawn)=4/52+13/52-1/52

P=16/52=4/13

or look at it this way...

P=13/52+3/52=16/52 because one of the aces, the ace of hearts, is already include in the 13/52

you add the probabilities because of the word "or"

the odds (in favor) of an ace or a heart is the ratio of the probability that the event will occur to the probability that the event will not occur

odds=(16/52)/(36/52)=16/36=4/9, or simply look at 4/13, 13-4=9, and the ratio is 4/9

the event cannot happen in 36 ways: 13 diamonds+13 spades+13 clubs-ace of diamonds-ace of spades-ace of clubs=39-3=36, so 16(ways it can happen)/36(ways it cannot happen)=16/36=4/9

note: don't be mislead looking at 4/9, it is not probability but odds; the event can happen in 4 ways and cannot happen in 9 ways, so the event can happen in 4 ways out of a total of 4+9=13 ways