A card is drawn from a standard deck of 52 cards. Find the probability that the card is either a five or heart

Question

I need help with the problem and how to get the answer 

Answer 1

Kenneth's answer looks right to me. In case you wanted more explanation of how to solve this, the problem is asking you to find the probability of one thing or another happening. You are asked to find the probability of either drawing a 5 or a heart. As Kenneth points out, there are 13 hearts (Ace, King, Queen, Jack, and numbers 2 through 10). So if you were just asked to find the probability of drawing a heart, it would be 13/52. But the problem also wants you to include (add) the probability of drawing a 5. There are four 5s in a deck, but you already included the 5 of hearts in 13/52. So you need to include the 3 other 5s (spades, clubs and diamonds). Adding up the probability of getting hearts OR 5s, you have 13/52 + 3/52 = 16/52.

You can reduce this fraction to 4/13. So that is your probability of drawing a heart or a 5. 

 

Whenever you do probability problems, check to see if you are being asked to find probability of one thing OR another, or of multiple events happening together. For instance, if this problem asked you to find the probability of drawing a heart AND a 5, well, there is only one 5 of hearts in a deck. So that would be 1/52.

 

Hopefully this (long) explanation helped! 

Answer 2

With 13 hearts in the deck, and three other cards (5s of spades, clubs and diamonds) in the definition of the Event,

P(E) = 16/52 = 4/13.