What is the probability of drawing a heart given the first card is a diamond?

The probability of drawing a heart given the first card is a diamond is 13/51.

When you draw a card from a standard deck of 52 cards, there are 13 hearts, 13 diamonds, 13 clubs, and 13 spades. If the first card you draw is a diamond, it means one of the 13 diamonds has been removed from the deck. This leaves 51 cards remaining in the deck.

Since the first card drawn is a diamond, it does not affect the number of hearts in the deck. There are still 13 hearts left. To find the probability of drawing a heart next, you need to consider the number of favourable outcomes (drawing a heart) over the total number of possible outcomes (the remaining cards in the deck).

The number of favourable outcomes is 13 (the number of hearts), and the total number of possible outcomes is 51 (the remaining cards). Therefore, the probability of drawing a heart given that the first card was a diamond is 13/51. This fraction represents the likelihood of the event happening and can also be converted to a decimal or percentage if needed, but for most GCSE Maths problems, leaving it as a fraction is perfectly acceptable.