A single card is selected from a deck of cards, Find the probability for it being a heart, given that it is red.
A deck of cards contains 52 cards, in which 26 are black and 26 are red ( 13 hearts and 13 diamonds).
Since we are told that the card is red, then we are going to ignore the 26 black cards, so, we have a 26 red card to choose from.
Now the probability that the selected card is heart is 13/26= 1/2
In other words, the chances of the card selected being heart is 50% since we only have 2 types (hearts and diamonds). So the card selected is either diamond or heart.
There are totally 52 cards.
There are 13 cards which are hearts.
We require the probability that a card drawn is heart with a condtion that the card is red. The redcards are 26 =13 harts+13 diamonds.
This is called Bay's conditional prbablity where you want the probabilty of an event under a special information or condtion.
We require P(H/R) = P(H&R)/P(R) , where H is the event of the selected card is heart and R is event that a selected card is red.And H/R is the event that theselected card is heat but with a given condition that it is red.
ThereforeP(H/R) = P(H&R)/P(R) = (13/52)/(26/52) = 13/26 =1/2