To get this equation you have to perform KCF which stands for Keep Change Flip. KCF is only to be used for division fraction problems. KCF means you Keep the first Fraction, then change the division sign into a multiplication sign. and last flip the last fraction.
Let be the event that the number on the first card is even.
Let be the event that the number on the second card is even.
The question is asking for the possibility that event and happen at the same time. However, whether occurs or not will influence the probability of . In other words, and are not independent. The probability that both and occur needs to be found as the product of
the probability that event occurs, and
the probability that event occurs given that event occurs.
5 out of the ten numbers are even. The probability that event occurs is:
.
In case A occurs, there will only be four cards with even numbers out of the nine cards that are still in the bag. The conditional probability of getting a second card with an even number on it, given that the first card is even, will be: