+13 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 the second card Grok draws has a multiple of
The probability of drawing an even number is 3/7. There are 3 even cards (2, 4, and 6) out of 7 total cards.
The probability of drawing a multiple of 3 is 2/7. There are 2 multiples of 3 (3 and 6) out of 7 total cards.
The probability of both of these events happening is 3/7 * 2/7 = 6/49.
Therefore, the probability that Professor Grok draws a card with an even number, and then a card that is a multiple of 3, is 6/49.
Here is the solution in more detail:
The probability of event A happening is the number of ways event A can happen divided by the total number of possible outcomes. In this case, event A is drawing a card with an even number. There are 3 even cards in the deck, so the probability of drawing an even card is 3/7.
The probability of event B happening is the number of ways event B can happen divided by the total number of possible outcomes after event A has already happened. In this case, event B is drawing a card that is a multiple of 3. There are 2 multiples of 3 in the deck, but one of them has already been drawn, so the probability of drawing a card that is a multiple of 3 after already drawing an even card is 2/6 = 2/7.
The probability of both events happening is the product of the probabilities of each event happening. In this case, the probability of drawing a card with an even number and then a card that is a multiple of 3 is 3/7 * 2/7 = 6/49.
