Assume that 2 cards are drawn from a

We are given a standard deck of 52 cards, and we want to find the probability of drawing two non-black cards without replacement. Let's begin by counting the number of non-black cards in the deck.
There are 26 black cards in the deck (13 spades and 13 clubs) and 26 non-black cards (13 hearts and 13 diamonds). If we draw a non-black card from the deck, there will be 51 cards left, 25 of which are non-black cards.
Now, let's use the multiplication rule of probability to find the probability of drawing a non-black card followed by another non-black card. The multiplication rule states that if two events A and B are independent, then the probability of both events occurring is the product of their individual probabilities.
So, let A be the event of drawing a non-black card on the first draw, and let B be the event of drawing a non-black card on the second draw. We want to find the probability of A and B occurring together.
Using the multiplication rule, we have:
$P(A\cap B)=P(A)·P(B\mid A)$
where $P(B\mid A)$ is the conditional probability of drawing a non-black card on the second draw given that a non-black card was drawn on the first draw.
Since we are drawing without replacement, the events A and B are not independent. After the first non-black card is drawn, there will be one less non-black card in the deck, so the probability of drawing another non-black card on the second draw will be affected.
To calculate the conditional probability $P(B\mid A)$, we can use the following formula:
$P(B\mid A)=\frac{\text{number of non-black cards left}}{\text{total number of cards left}}$
After the first non-black card is drawn, there will be 25 non-black cards left out of a total of 51 cards left in the deck. Therefore:
$P(B\mid A)=\frac{25}{51}$
Now, we can substitute the values of $P(A)$ and $P(B\mid A)$ into the multiplication rule formula to find the probability of drawing a non-black card followed by another non-black card:
$P(A\cap B)=P(A)·P(B\mid A)=\frac{26}{52}·\frac{25}{51}=\frac{25}{102}$
Therefore, the probability of drawing two non-black cards without replacement, where the first card is non-black and the second card is also non-black, is $\frac{25}{102}$.