In Ms. Q's deck of cards, every card is one of four colors (red, green, blue, and yellow), and is labeled with one of seven numbers (1, 2, 3, 4, 5, 6, and 7). Among all the cards of each color, there is exactly one card labeled with each number. The cards in Ms. Q's deck are shown below.


Professor Grok draws two cards from Ms. Q's deck at random without replacement. What is the probability that the first card Grok draws has an even number and is blue, and the second card Grok draws has an odd number and is red?

 Dec 28, 2022

The probability of Grok first drawing a even blue card is \(\frac{3}{7} \cdot \frac{1}{4} = \frac{3}{28}\). The probability of Grok drawing an even red card is \(\frac{4}{7} \cdot \frac{1}{4} = \frac{4}{28} = \frac{1}{7}\). However, he took a card already, so the probability is actually \(\frac{4}{27}\). So, the probability is \(\frac 3 {28} \cdot \frac 4 {27} = \frac 1{63}\)

 Dec 28, 2022

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