What is the probability that after pulling out of a card deck 3 heart cards, that the 4th card will be also a heart? There are 52 cards in the deck and there is no replacement.
$$P(4\text{th heart} | 3 \text{ first hearts}) = \frac{P(4\text{th heart}\cap 3\text{ first hearts})}{P(3\text{ firsthearts})}$$
How do you calculate this probability:
$P(4\text{th heart}\cap 3\text{ first hearts})$
Best Answer
You are overcomplicating things. You can use the more intuitive meaning of conditional probability
Well, if you know that the first three cards were hearts, then the probability that the fourth card will be a heart is equal to the probability of drawing a heart out of a deck of $49$ cards of which $10$ are hearts.
Of course, you can also go with the original attempt. Then the event
Is the same event as