If you draw one card from a normal deck of cards, what is the probability that it will be a Jack, Queen, King, heart or diamond?

To understand the probability of drawing a Jack, Queen, King, heart, or diamond from a standard 52-card deck, we first need to count the number of cards that fit these criteria. A standard deck contains four suits: hearts, diamonds, clubs, and spades, with 13 cards in each suit. Among these, hearts and diamonds are red suits, while clubs and spades are black. Each suit also contains three face cards: a Jack, a Queen, and a King.

When calculating probabilities involving "or," it's important to avoid double-counting. There are 13 hearts and 13 diamonds, totaling 26 red cards. These 26 cards already include the Jack, Queen, and King of hearts, and the Jack, Queen, and King of diamonds. So, the face cards from the red suits are already accounted for. We then need to add the remaining face cards from the black suits (clubs and spades). There are three face cards (Jack, Queen, King) in clubs and three face cards in spades.

Therefore, the total number of favorable outcomes is the sum of the red cards (hearts and diamonds) plus the face cards from the black suits. This gives us 13 (hearts) + 13 (diamonds) + 3 (Jack, Queen, King of clubs) + 3 (Jack, Queen, King of spades) = 32 unique cards. Since there are 52 cards in a standard deck, the probability of drawing one of these favorable cards is 32 out of 52.

This fraction, 32/52, can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4. This simplifies the probability to 8/13. As a decimal, this is approximately 0.615, or 61.5%. Understanding how to categorize and count specific cards, especially when categories overlap, is a fundamental skill in probability. It illustrates the "addition rule" for probabilities, where you sum individual probabilities and subtract any overlaps to ensure each outcome is counted only once.