There are two decks of cards. Each deck has a red, a yellow, a blue, and a green card in it. If a card is drawn, from the first deck, and then a second card drawn from the second deck, what is the probability that a red card and green card are drawn (not necessarily in that order)? Round your answer to two decimal places.

Question

There are two decks of cards. Each deck has a red, a yellow, a blue, and a green card in it. If a card is drawn, from the first deck, and then a second card drawn from the second deck, what is the probability that a red card and green card are drawn (not necessarily in that order)? Round your answer to two decimal places.

and

There are two decks of cards. Each deck has a red, a yellow, a blue, and a green card in it. If a card is drawn, from the first deck, and then a second card drawn from the second deck, what is the probability that a red card or green card is drawn (not necessarily in that order)? Round your answer to two decimal places.

Answer 1

you can list the sample space by hand, only 16 outcomes (4 colors * 4 colors)

r/g or g/r are 2 of 16 possibilities ... .13

red and green make up half of the cards

the probability of drawing two cards with no red or green is ... 1/2 * 1/2

the compliment is ... 3/4 ... .75

Answer 2

To find the probability of certain events occurring, we will need to determine the total number of possible outcomes and the number of favorable outcomes.

For the first question, we want to find the probability of drawing a red card and a green card. There are two decks of cards, each containing four cards. Therefore, the total number of possible outcomes is 4 * 4 = 16.

Now, let's consider the favorable outcomes. We can obtain a favorable outcome in two ways: either drawing a red card first and then a green card, or drawing a green card first and then a red card.

The probability of drawing a red card and then a green card can be calculated as follows:
- For the first card, there are 4 options (red, yellow, blue, green), and we want to draw a red card (1 favorable outcome).
- After drawing a red card from the first deck, there is 1 green card left in the second deck, so the probability of drawing a green card is 1/4.

To find the probability of both events happening, we need to multiply the probabilities calculated above:
P(red and green) = (1/4) * (1/4) = 1/16

Now, since we can also obtain a favorable outcome by drawing a green card first and then a red card, the total probability is:
P(red or green) = P(red and green, not necessarily in that order) * 2 = (1/16) * 2 = 1/8

Therefore, the probability of drawing a red card or a green card (not necessarily in that order) is 1/8, which is equivalent to 0.13 when rounded to two decimal places.