A container contains two red, three yellow, and four green cards. Two cards are selected at random, one after the other and with replacement, from the container. Calculate the probability that both cards are yellow.
The probability of selecting a yellow card on the first draw is 3/9 since there are 3 yellow cards out of a total of 9 cards. After replacing the card, the probability of selecting a yellow card on the second draw is also 3/9.
The probability of both events happening is the product of their individual probabilities, so the probability of selecting two yellow cards is (3/9) * (3/9) = 9/81 = 1/9.
Therefore, the probability that both cards selected are yellow is 1/9.
In order to calculate the probability that both cards selected are yellow, we need to determine the probability of drawing a yellow card on each individual draw, and then multiply these probabilities together.
Step 1: Determine the probability of drawing a yellow card on the first draw.
There are a total of 2 + 3 + 4 = 9 cards in the container, and 3 of them are yellow. Therefore, the probability of drawing a yellow card on the first draw is 3/9 = 1/3.
Step 2: Determine the probability of drawing a yellow card on the second draw.
Since the cards are replaced after each draw, the probability of drawing a yellow card on the second draw is also 1/3.
Step 3: Multiply the probabilities together.
To calculate the probability of both cards being yellow, we multiply the probabilities of each step together: (1/3) * (1/3) = 1/9.
Therefore, the probability that both cards selected are yellow is 1/9 or approximately 0.1111.
To calculate the probability of selecting two yellow cards, you need to know the total number of cards in the container and the number of yellow cards.
First, let's find the total number of cards in the container:
Total cards = Number of red cards + Number of yellow cards + Number of green cards
= 2 + 3 + 4
= 9
Next, let's find the probability of selecting the first yellow card:
Probability of selecting a yellow card on the first draw = Number of yellow cards / Total cards
= 3 / 9
= 1/3
Since we are replacing the cards after each draw, the probability remains the same for the second draw.
Therefore, the probability of selecting a yellow card on the second draw is also 1/3.
To find the probability of both cards being yellow, we need to multiply the probabilities of selecting a yellow card on the first and second draws:
Probability of both cards being yellow = Probability of first yellow card * Probability of second yellow card
= (1/3) * (1/3)
= 1/9
So, the probability that both cards selected are yellow is 1/9.