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In Janice'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 Janice's deck are shown below.

a) Ella draws two cards from Janice's deck at random without replacement. What is the probability that the first card Ella draws has an even number, and the second card Ella draws has an odd number?

b) Ella draws two cards from Janice's deck at random without replacement. What is the probability that the first card Ella draws has an even number, and the second card Ella draws has a multiple of 3?

Nov 2, 2023

#1
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a) Probability that the first card has an even number and the second card has an odd number

There are 14 even cards and 14 odd cards in Janice's deck. So, the probability that the first card Ella draws has an even number is 14/28.

Once Ella draws the first card, there are only 27 cards left in the deck. Since Ella is not replacing the first card, there are now 13 even cards left in the deck. So, the probability that the second card Ella draws has an odd number is 13/27.

Therefore, the probability that the first card Ella draws has an even number and the second card Ella draws has an odd number is:

(14/28) * (13/27) = 13/54

b) Probability that the first card has an even number and the second card has a multiple of 3

There are 14 even cards in Janice's deck, and 7 of them are multiples of 3 (2, 4, 6, 8, 10, 12, and 14). So, the probability that the first card Ella draws has an even number and is a multiple of 3 is 7/28.

Once Ella draws the first card, there are only 27 cards left in the deck. Since Ella is not replacing the first card, there are now 6 even cards left in the deck, and 3 of them are multiples of 3 (4, 8, and 12). So, the probability that the second card Ella draws is a multiple of 3 is 3/27.

Therefore, the probability that the first card Ella draws has an even number and the second card Ella draws has a multiple of 3 is:

(7/28) * (3/27) = 1/36.

Nov 3, 2023
#2
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Thank you for your help but both answers are wrong. I believe in your solutions you might be overcounting, and also my math said the answers were wrong.

Keihaku  Nov 3, 2023
edited by Keihaku  Nov 3, 2023