Question
A container contains two red, three yellow, and four green cards. Two cards are selected at random, one after the other and without replacement, from the container. Calculate the probability that one card is red and one card is yellow.
Answers
GPT 3.5
To calculate the probability that one card is red and one card is yellow, we need to determine the total number of possible outcomes and the number of favorable outcomes.
First, let's calculate the total number of possible outcomes:
There are 9 cards in total (2 red + 3 yellow + 4 green).
For the first card, we have 9 options. After selecting one card, there are 8 cards left for the second selection.
Therefore, the total number of possible outcomes is 9 * 8 = 72.
Next, let's determine the number of favorable outcomes:
To have one card red and one card yellow, we can choose a red card first and then a yellow card or vice versa.
For the first selection, we have 2 red cards to choose from. After selecting one red card, there are 3 yellow cards left for the second selection. So we have 2 * 3 = 6 favorable outcomes.
Alternatively, we could first select a yellow card then a red card. Again, we have 3 options for the first selection. After selecting one yellow card, there are 2 red cards remaining. So there are 3 * 2 = 6 favorable outcomes.
Adding these two possibilities together, we have a total of 6 + 6 = 12 favorable outcomes.
Finally, let's calculate the probability:
The probability is given by the number of favorable outcomes divided by the total number of possible outcomes.
Therefore, the probability that one card is red and one card is yellow is 12/72, which simplifies to 1/6.
So the probability is 1/6 or 0.1667 (rounded to four decimal places).
First, let's calculate the total number of possible outcomes:
There are 9 cards in total (2 red + 3 yellow + 4 green).
For the first card, we have 9 options. After selecting one card, there are 8 cards left for the second selection.
Therefore, the total number of possible outcomes is 9 * 8 = 72.
Next, let's determine the number of favorable outcomes:
To have one card red and one card yellow, we can choose a red card first and then a yellow card or vice versa.
For the first selection, we have 2 red cards to choose from. After selecting one red card, there are 3 yellow cards left for the second selection. So we have 2 * 3 = 6 favorable outcomes.
Alternatively, we could first select a yellow card then a red card. Again, we have 3 options for the first selection. After selecting one yellow card, there are 2 red cards remaining. So there are 3 * 2 = 6 favorable outcomes.
Adding these two possibilities together, we have a total of 6 + 6 = 12 favorable outcomes.
Finally, let's calculate the probability:
The probability is given by the number of favorable outcomes divided by the total number of possible outcomes.
Therefore, the probability that one card is red and one card is yellow is 12/72, which simplifies to 1/6.
So the probability is 1/6 or 0.1667 (rounded to four decimal places).