There are two events we need to consider:
Event 1: Drawing an even number first.
There are 4 colors in the deck.
Each color has one even number (2, 4, or 6).
So, there are 4 * 3 = 12 cards that satisfy this condition (even number, any color).
Event 2: Drawing a multiple of 3 after drawing an even number (without replacement).
After drawing the first card, there are only 27 cards remaining.
There are 3 multiples of 3 left (3 and 6, since one even number - 6 - is already drawn).
However, since Grok isn't replacing the first card, there are only 2 colors left that have multiples of 3 (red and blue, as the even number 6 was likely green or yellow).
Therefore, there are 2 * 1 = 2 cards that satisfy this condition (multiple of 3, remaining colors).
Total Favorable Cases:
To get the probability, we need the number of favorable cases (both events happening) divided by the total number of possible cases (drawing any two cards).
Favorable cases: 12 (Event 1) * 2 (Event 2) = 24
Total possible cases: There are 28 cards total (7 numbers * 4 colors), and we draw 2 without replacement. So, the total number of possible choices is 28C2 (28 choose 2) which is 28 * 27 / (2 * 1) = 378
Probability:
Therefore, the probability that Professor Grok draws an even number first, followed by a multiple of 3 (without replacement), is:
Probability = Favorable Cases / Total Possible Cases Probability = 24 / 378
Simplifying the fraction:
Both the numerator (24) and denominator (378) have a common divisor of 6. We can simplify:
Probability = (24 / 6) / (378 / 6) Probability = 4 / 63
So, the probability is 4/63.
